MANUAL 


COUNTERPOINT 


BY 


S.  JADASSOHN 

PROFESSOR    IN    THE    ROYAI-    CONSERVATORY    OF    MUSIC    AT    LEIPZIG. 


BY 


DR.  TH.    BAKER. 


SIXTH  EDITION 


NEW   YORK: 
G.    SCHIRMER. 


COPYRIGHT,  1902,  BY  G.  SCHIRMER. 


16117 


PREFACE. 


THIS  Manual  forms  an  introduction  to  the  study  of  single,  double, 
triple  and  quadruple  counterpoint  in  the  strict  style.  All  rules, 
directions,  principles  and  observations  contained  in  the  book,  are 
founded  on  the  contrapuntal  style  of  Bach,  Handel,  and  other  classic 
masters  who  followed  our  tonal  system  of  major  and  minor  keys  in 
their  writings. 

The  aim  of  the  pupil's  studies  in  counterpoint  is,  to  prepare  him 
for  the  study  of  canon  and  fugue ;  but  even  the  disciple  of  art  who 
does  not  intend,  or  is  not  able,  to  become  a  composer,  will  be  enabled 
by  such  study  to  penetrate  deeper  into  the  works  of  the  classic  mas- 
ters, and  better  to  apprehend  the  sublimest  creations  of  their  art. 
But  let  no  one  imagine  that  in  a  course  of  contrapuntal  study  it  suf- 
fices only  to  read  or  learn  the  rules  ;  this  could  be  done  very  easily 
and  quickly.  True  progress  can  be  made  in  this,  as  in  all  other  dis- 
ciplines of  art,  only  by  dint  of  serious  and  conscientious  work.  Not 
until  the  student  shall  have  worked  out  the  exercises  contained  in  the 
Manual  in  proper  sequence  and  with  due  attention,  will  he  be  pre- 
pared to  proceed  to  the  study  of  Canon  and  Fugue. 

S.  JADASSOHN. 
Leipzig,  August,  1883. 


PREFACE  TO   THE   THIRD   EDITION. 


rnOGETHER  with  the  Third  Edition,  a  considerable  number  of 
"  Exercises  and  Examples  for  the  Studies  in  Counterpoint"  have 
been  published  separately.  Both  teachers  and  students  will  find  them 
of  practical  utility  when  used  in  conjunction  with  the  exercises  given 
in  the  Manual  itself. 

S.  JADASSOHN. 
Leipzig,  October,  1896. 


111 


iv 


TABLE  OF  CONTENTS. 


PART  THE   FIRST. 

SINGLE    COUNTERPOINT. 

CHAPTER  I. — Equal  Counterpoint  in  Four-part  Writing.     Page 
1  to  13. 

§  1.  Cantus  firmus  in  the  bass.  §  2.  Cantus  firmus  in  the  soprano. 
§  3.  Cantus  firmus  in  the  inner  parts.  Exercises. 

CHAPTER  II. — Unequal  Counterpoint.     Page  13  to  26. 

£§4,  5,  6,  7,  and  8.  Counterpoint  of  two  notes  in  the  bass  against 
one  in  the  cantus  firmus.  Illustrations.  Exercises. 

CHAPTER  III. — Counterpoint  in  the  Higher  Parts.      Page  26 
to  50. 

§10.  Rules.  Illustrations.  $11.  Counterpoint  in  the  Soprano. 
§12.  Cantus  firmus  in  the  inner  parts.  Illustrations.  Exercises. 
§13.  Counterpoint  in  the  alto  or  tenor.  Illustrations.  Exercises. 
§14.  The  counterpoint  in  several  parts  alternately  and  simultane- 
ously. Illustrations.  Exercises. 

CHAPTER  IV. — Counterpoint  of  Four  Notes  against  One  in  the 
Cantus  Firmus.     Page  50  to  60. 

§15.  The  counterpoint  in  one  part.  Illustrations.  Exercises. 
§  16.  The  counterpoint  in  two  or  more  parts. 

CHAPTER  V. — Three-part  Counterpoint.     Page  61  to  67. 

§  17.  Equal  counterpoint  in  a  three-part  movement ;  the  contra- 
puntal movement  of  two  notes  against  one  in  the  cantus  firmus. 
Illustrations.  §18.  Contrapuntal  movement  of  four  notes  against 
one  in  the  cantus  firmus.  Illustrations.  Exercises. 

CHAPTER  VI. — Two-part  Counterpoint.     Page  68  to  71. 
§19.  Rules.     Illustrations.    Exercises. 


TABLE    OF  CONTENTS.  V 

PART   THE   SECOND. 
DOUBLE   COUNTERPOINT. 

CHAPTER  VII.— Page  72  to  83. 

§20.  Double  counterpoint  in  the  octave,  with  two  parts.  $21. 
Double  counterpoint  in  three-part  writing.  Inversion  of  the  two 
highest  parts.  §22.  Inversion  of  the  two  lowest  parts.  Illustra- 
tions. Exercises. 

CHAPTER  VIII.— Page  84  to  92. 

§  23.  Double  counterpoint  in  the  octave,  in  four-part  writing.  In- 
version of  two  parts,  soprano  and  tenor,  soprano  and  alto,  alto  and 
tenor,  tenor  and  bass,  bass  and  soprano,  accompanied  by  two  free 
parts.  Illustrations.  Exercises. 

CHAPTER  IX. — Triple  Counterpoint  in  the  Octave,  in  Three- 
and  Four-part  Writing.     Page  92  to  105. 

§ 24.  Three-part  illustrations  with  five  inversions.  Four-part  illus- 
tration to  a  given  bass:  the  three  highest  parts  inverted  five  times. 
Exercises.  §25.  Quadruple  counterpoint  in  the  octave,  with  23  in- 
versions. Illustration,  and  inversions  of  the  same.  Exercises. 

CHAPTER  X. — Double  Counterpoint  in  the  Tenth  and  Twelfth. 
Page  105  to  118. 

§  26.  Rules.  Illustration  in  two  parts,  with  inversions ;  likewise  in 
three  parts,  in  various  modes.  Illustrations.  Four-part  illustration 
for  23  inversions.  Practical  application  of  double  counterpoint  in 
the  tenth  by  Bach.  §  27.  Double  counterpoint  in  the  twelfth.  Ex  - 
planation.  Rules.  Illustration  with  inversions ;  the  same,  with  one 
or  two  free  parts. 


PART   THE   THIRD. 

COUNTERPOINT    IN    FIVE,    SIX,    SEVEN    OR    EIGHT 
REAL    PARTS. 

CHAPTER  XL— Page  119  to  137. 

§  28.  Writing  with  five  parts.  Illustrations.  §  29.  Six-part  writing. 
Illustrations.  §30.  Seven-part  writing.  Illustrations.  §31.  Eight- 
part  writing.  Illustrations. 


PART   THE   FIRST. 

SINGLE    COUNTERPOINT. 


CHAPTER    I. 
Equal  Counterpoint. 

§1.  Under  the  term  "Counterpoint"  we  understand  the  inde- 
pendent leading  of  one  or  several  melodic  parts,  in  similar  or  contrary 
motion,  with  an  observance  of  a  natural  and  correct  chord-progression. 
The  essence  of  counterpoint  is,  therefore,  melodic  ;  each  of  the  melo- 
dies thus  combined  should  be  independently  led,  and  each  should  be 
on  a  par  with  the  rest  as  a  member  of  the  Whole.  This  principle 
results,  in  duple,  triple,  and  quadruple  counterpoint,  in  the  ability  to 
let  the  two,  three,  or  four  contrapuntal  parts  exchange,  at  pleasure, 
their  mutual  positions.  Thus,  each  part  may  become,  in  turn,  so- 
prano, alto,  tenor,  or  bass. 

In  the  course  of  our  exercises  in  harmony,  which  had  to  do,  pri- 
marily, with  the  structure  and  progressions  of  chords,  we  have  already 
recommended  that  the  student  should  give  some  care  and  attention  to 
the  leading  of  the  parts  in  a  melodic  sense.  The  last  exercises  in  the 
Manual  of  Harmony  were  especially  devoted  to  the  development  of 
the  bass  and  the  soprano.  Consequently,  beginning  where  these 
exercises  left  off,  we  may  now  commence  those  in  single  counterpoint. 
A  distinction  is  made  between  Equal  Counterpoint,  in  which  only 
notes  of  the  same  time- value  are  set  to  a  cantus  firm  us,  and  Unequal 
Counterpoint,  in  which  notes  of  different  time-value  are  opposed, 
either  in  one  part  or  in  several  parts,  to  those  of  the  cantus  firmus. 
In  equal  counterpoint,  the  leading  of  the  parts  will  be  only  melodically 
independent ;  in  unequal  counterpoint,  it  will  be  independent  both 
melodically  and  rhythmically. 

When  other  parts  are  added,  in  equal  counterpoint,  to  a  cantus 
firmus,  this  exercise  is  distinguished  from  the  last  ones  in  harmony 
simply  by  the  circumstance,  that  the  choice  of  the  chords  is  free. 
This  renders  it  possible,  however,  to  pay  more  particular  attention  to 
the  independent  melodic  leading  of  each  and  every  part. 

We  again  begin  with  exercises  in  four-part  writing,  giving  a  can- 
tus firmus  in  the  bass,  to  which  the  student  is  now  to  add  the  three 


2  EQUAL    COUNTERPOINT. 

higher  parts  in  several  different  ways,  selecting  not  only  different 
positions  and  inversions,  but  also  different  chords.  For  the  first  few 
times  of  working  out  a  cantus  firmus,  only  chords  proper  to  the  key 
should  be  used ;  the  student  will  also  do  well  to  choose,  at  first,  as 
simple  harmonies  as  possible,  passing  over  very  gradually  to  the  em- 
ployment of  the  more  unusual  chords.  Only  after  one  and  the  same 
cantus  firmus  has  been  worked  out  several  times  with  different  chords 
proper  to  the  key,  should  one  proceed  to  introduce  modulatory  effects  ; 
and  these  latter  must  not  lead  too  far  away,  or  appear  forced,  or  as  a 
straining  after  effect.  To  illustrate  the  foregoing,  we  append  various 
workings-out  of  the  following  bass : 

Cantus  firmus. 


PI 


NOTE. — The  student  ought  always  to  write  out  his  exercises  in  four  different  clefs. 
Our  examples  are  written  on  two  staves  merely  to  save  room.  [The  ties  mark  the 
preparation  of  dissonances.] 


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3. 


266 


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CANTUS  FIRMUS  IN  BASS. 


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EQUAL    COUNTERPOINT. 


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CANTOS  FIRM  US  IN  BASS. 


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In  the  bass  given  above,  only  the  six  notes  of  the  second,  third, 
fourth,  fifth,  sixth  and  seventh  measures  permit  a  variation  in  the 
harmony ;  the  chords  in  the  first  and  closing  measures  must  neces- 
sarily be  the  tonic  triad  ;  that  of  the  measure  before  the  last  must  be 
the  dominant  chord,  to  prepare  the  close.  Nevertheless,  this  cantus 
firmus  admits  of  a  great  number  of  different  workings-out.  The  first 
two  of  the  above  examples  contain  only  triads  ;  in  the  third  and  eighth 
the  dominant  seventh-chord  is  employed ;  in  Xos.  4,  5,  6,  7,  11,  12, 
and  13,  subordinate  chords  of  the  seventh  proper  to  the  key  are  used  ; 
in  Nos.  9  and  10  we  find  the  subordinate  seventh-chords  on  the  2nd 
and  7th  degrees  in  C  major,  with  altered  root  and  altered  third  ;  only 
the  last  three  examples  show  a  transient  modulation  to  the  dominant 
triad  in  a  minor,  in  which,  of  course,  the  chromatic  alteration  occurs 
in  the  same  part  (alto),  to  avoid  the  inharmonic  relation.  This  can- 
tus firmus  would  also  permit  other  developments  ;  those  given  above 
will  suffice,  however,  to  show  the  pupil  how  the  exercises  are  to  be 
worked  out.  But  it  is  not  necessary  to  begin  by  working  out  the 
following  given  basses  only  in  triads,  as  was  done  in  Examples  1  and  2. 


EQUAL    COUNTERPOINT. 

Exercises. 


-1*- -*--»--* 


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2 

1 

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As  an  aid  to  the  student,  a  few  beginnings  for  the  working-out  of 
given  bass  No.  17  are  appended. 


CANT  US  FIRM  US  IN  BASS. 


26.  / 


fe 


Ivor 


I 


-s,. 

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etc. 


etc. 


ii^ 


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etc. 


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etc. 


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4  etc. 

3  6  7 


etc. 


1 


From  the  beginnings  shown  in  No.  26,  the  student  will  perceive 
that  this  same  bass  may  be  worked  out  in  very  many  other  forms. 


8  EQUAL    COUNTERPOINT. 

The  Cantus  Firmus  in  the  Soprano. 

§  2.  We  now  give  a  cantus  firmus  in  the  soprano  ;  the  leading  of 
the  bass  requires,  in  this  case,  the  greatest  attention.  (See  Manual  of 
Harmony,  §61.)  No  new  rules  are  needed  here ;  as  a  practical  guide, 
the  beginning  of  cantus  firmus  No.  31  is  worked  out  below  in  several 
forms. 


27. 


etc. 


28. 


a. 

GX 

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etc. 

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— gy^^-j~.r^g!! 
Z3ar3C 


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t^ 


etc. 


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etc. 

s=l 


CANTUS  FIRMUS  IN  SOPRANO. 

Exercises. 

^3      ~&~    -<9-     n 


29.- 


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30. 


31.  F=^&— * 


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36. 


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1 

Exercises  Nos.  30,  32,  34  and  36  contain  the  leading-notes  of  the 
minor  scales  concerned,  and  are,  of  course,  to  be  worked  out  in  minor. 


10 


EQUAL    COUNTERPOINT. 


It  is  evident,  from  the  note  Z>#  in  the  fifth  measure,  that  cant  * 
firmus  No.  34  is  to  be  worked  out  in  e  minor.  We  give  the  following 
by  way  of  illustration. 


C.  f. 

-y-S—  —  <=*= 

^  ^  

ps 

E 

U^         '^ 

?p  - 

—  &  

34 
fa). 

W:^~~<5>  — 

=s  —  1 

6 
5 

6 

2 

5 

y^A  «^i 

*& 

^       \ 

[^/•Jr/li          ^X 

"*'          1      ^^  — 

* 

^^    v  y 

IVT          vn°7 


1 

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/^ 



—  —  

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tr    -g. 

6 

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6 
4 

S3 

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5 

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1 

~*%- 

1 
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a 

—  (51  

1 

= 





<Ci 

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n°T 


A  working   of   cantus  firmus  No.  35  might  be  presented  in  the 
following  form : 

N.B. 

"    5-5- r-— r-^i <—<S> , 


C  f. 


35 

fa). 


2? 


=%+ 


IV 


IV 


N.  B. — The  seventh  must  be  led  upward,  because  its  natural  tone  of  resolution  is 
taken  by  the  bass.     (Compare,  concerning  this  point,  Manual  of  Harmony,  §  45.) 


f?  ~\         & 


6  6 


VII0 


V, 


CANT  US  FIRM  US  IN  THE  INNER  PARTS. 


11 


The  Cantus  Firmus  in  the  Inner  Parts. 

§3.  It  is  far  more  difficult  to  add  contrapuntal  parts  to  a  cantus 
firmus  set  in  the  alto  or  tenor,  than  to  the  same  in  one  of  the  outer 
parts-  Although  the  leading  of  the  inner  parts,  in  any  four-part 
movement,  ought  to  be  melodicaily  independent,  it  must,  when  the 
cantus  firmus  is  in  one  of  the  outer  parts,  necessarily  have  a  smooth, 
even  character  ;  because  the  inner  parts,  frequently  restricted  in  scope 
by  the  outer  parts,  cannot  move  with  the  same  freedom  of  melodic 
development  as  the  soprano  and  the  bass.  Now,  if  the  principal  mel- 
ody, the  cantus  firmus,  be  set  in  an  inner  part,  the  leading  of  the 
soprano  is  the  chief  point  which  we  have  to  consider.  This  highest 
part  must  never  exhibit  the  smooth,  even  progression  and  character  of 
an  inner  part.  (Touching  this  point,  compare  Manual  of  Harmony, 
§61.)  A  working-out  of  an  example  with  the  cantus  firmus  given  to 
the  alto,  such  as  is  found  in  No.  37,  would  be  unskilful  in  the 
extreme. 


03  /  * 

^x 

f^ 

^ 

—  0  tZ 

*  .  \ 

37.   ( 


The  above  example  may  easily  be  improved  by  letting  soprano 
and  tenor  exchange  places ;  in  which  form  it  appears  in  No.  38. 


38.  / 


s 


I3?I 


Below  are  given  two  further  illustrations  with  the  same  cantus 
firmus  in  the  alto.  In  these  the  tenor  has  a  more  melodic  leading 
than  in  No.  38,  where  it  appears  merely  as  the  inversion  of  a  soprano 
led,  intentionally,  as  unskilfully  as  possible. 


12 


EQUAL    COUNTERPOINT. 


39  a. 


\-^—\-<s>- 


II 


39  &. 


& 

i 

22 

o 

1 

The  following  exercises  are  for  a  cantus  firmus  set  in  the  alto  or 
tenor.  Too  much  time  must  not,  however,  be  spent  upon  such  work. 
The  student  will  not  attain  perfect  facility  till  later,  after  he  has 
learned  to  solve  more  complicated  contrapuntal  problems. 

Exercises. 

THE  CANTUS  FIRMUS  IN  THE  ALTO. 


4O. 


-<&- 


42. 


iJ. 


_/2 *=> 


-,5,.       -ffl- 


2 ,£>_ _ e, <5,__ 


CANTUS  FIRMUS  IN  TENOR. 


13 


iT-^  fartr 


44. 


THE  CANTUS  FIEMUS  IN  THE  TENOB. 


45. 


CHAPTEK    II. 
Unequal  Counterpoint. 

§  4.  In  equal  counterpoint,  the  leading  of  the  several  parts  is  in- 
dependent only  in  a  melodic  sense.  In  unequal  counterpoint,  the 
independence  of  the  parts  is  essentially  increased  by  the  greater  free- 
dom in  rhythmic  movement  of  one  or  more  parts  opposed  to  the  cantus 
firmus.  Students  were  formerly  required  to  write  two,  three,  four, 
six,  or  even  eight  notes  to  one  note  in  the  cantus  firmus,  and  to  prac- 
tise this,  at  first,  by  giving  the  more  rapid  movement  to  only  one  part 
at  a  time.  It  is  sufficient,  however,  for  the  student  to  write,  at  first, 
two  notes,  and  then  four  notes,  to  one  in  the  cantus  firmus.  All  other 
forms  of  movement,  in  duple  and  triple  time,  are  derivable  from  these 
two  simple  forms.  On  the  other  hand,  we  retain  the  method  of  giving 
the  rapid  movement  to  one  part  at  a  time ;  though  in  practice  it  more 
frequently  happens  that  several  parts  have  it  either  simultaneously  or 
alternately.  True,  it  is  more  difficult  to  keep  up  this  movement  in 
one  part  alone,  but  for  that  very  reason  the  attention  will  be  directed 
to  the  leading  of  each  separate  part.  After  the  student  has  practised 
the  movement  with  each  part  by  itself,  it  will  be  an  easy  matter  for 
him  to  write  a  free  and  flowing  movement,  now  in  all  the  parts  to- 
gether, and  again  passing  from  one  to  the  other,  to  a  given  cantus 
firmus. 


14 


UNEQUAL   COUNTERPOINT. 


We  begin  by  giving  the  bass  two  notes,  against  one  in  the  cantus 
firmus.  Each  note  of  the  counterpoint  should  be  a  simple  chord- 
note.  Suspensions,  even  when  well  prepared  (by  a  leap),  can  be  but 
rarely  employed.  They  are  best  introduced  at  the  beginning,  or  just 
before  the  close  of  the  exercise  ;  e.  g. , 


Beginning. 


Close. 


49. 


-&- 


In  the  midst  of  the  movement,  the  introduction  of  even  a  well- 
prepared  suspension  has  a  disagreeable  effect,  because  it  checks  the 
movement  of  the  bass.  We  learned,  in  the  harmony-course,  that  a 
suspension  in  the  bass  can,  in  most  cases,  be  employed  only  before 
the  third  of  a  chord. 

Now,  if  a  suspension,  as  being  a  check  to  the  movement,  is  to  be 
employed  very  rarely  and  cautiously  in  the  counterpoint  of  the  bass, 
it  will  be  readily  perceived  that  the  tying  of  a  note  in  a  chord  to  the 
same  note  in  the  following  harmony  must  be  sedulously  avoided. 
There  remain,  consequently,  only  the  three  following  resources  for  the 
leading  of  the  bass  : 

1.  By  a  leap  from  one  tone  to  another  in  the  same  chord. 

2.  Into  the  seventh  of  any  seventh -chord,  this  seventh  entering 

on  the  weak  beat  as  a  passing-note  with  descending  pro- 
gression. 

3.  Into  the  root  of  any  seventh-chord,  this  root  entering  on  the 

weak  beat  by  a  leap  from  a  chord  of  the  sixth. 

These  three  ways  of  leading  the  bass  are  shown,  in  two  different 
combinations,  in  the  examples  below. 


5O. 


C:   I 


COUNTERPOINT  IN  THE  BASS. 


15 


The  last  measure  of  No.  50  b  shows  that  it  is  allowable  to  leave 
out  the  third  of  the  chord  on  the  second  (weak)  beat ;  but  it  should 
never,  in  triads,  be  omitted  on  the  strong  beat,  and,  in  seventh-chords, 
only  in  very  exceptional  cases. 

Occasionally,  too,  the  bass  may  leap  from  the  root  of  a  triad  to  the 
root  of  a  seventh-chord  on  the  weak  beat ;  provided,  that  the  aim  of 
this  leading  is  not  merely  to  cover  up  incorrect  consecutive  octaves  by 
retarding  them.  Ex.  51  a  is  quite  correct ;  but  Ex.  51  6  is  inadmissible. 


a.  good. 


6.  bad. 


The  open  consecutive  octaves  and  fifths  over  the  bar,  which 
would  result  but  for  the  leap  in  the  bass,  are  not  covered  even  by  this 
wide  leap  of  a  sixth.  Counterpoint  like  that  in  Ex.  52,  below,  is  not 
to  be  tolerated. 


bad. 


52. 


The  contrapuntal  movement  does,  however,  neutralize  the  retarded 
consecutive  octaves  in  certain  cases.  This  often  occurs  when  the  bass 
leaps,  from  the  position  of  the  sixth-chord  (of  the  triad)  into  the  root 
of  a  seventh -chord.  When  the  leading,  in  such  cases,  is  in  contrary 
motion,  the  effect  is  good,  more  especially  when  two  chords  of  the 
seventh  are  connected  (53  a) . 


a.  good. 


6.  good. 


c.  not  so  good.  d.  bad. 


53. 


? 1-        I     '    -r 1 

i 1 <S> — l-iS 1 ^5 — I 

_ sLl_Jb  =3^3 


16 


UNEQUAL    COUNTERPOINT. 


§5.  More  than  three  notes  belonging  to  one  and  the  same  har- 
mony, and  progressing  in  the  same  direction,  should  not  be  written 
consecutively  in  the  counterpoint.  The  leading  of  the  bass  in  Ex.  54 
is  bad. 


54. 


Here  the  bass  takes,  in  the  same  direction,,  the  notes  C-E-G-B  (sev- 
enth-chord on  the  1st  degree  in  C  major),  then  C-A-F-D  (n7),  A-F- 
D-B  (vn°7),  and  F-D-B-G  (V7).  Such  progressions  must  always  be 
carefully  avoided.  At  the  close  (measure  before  the  last),  the  bass 
may  take  with  good  effect  a  leap  of  an  octave,  best  from  above  down- 
ward, but  also  from  below  upward.  At  the  beginning,  too,  an  octave- 
leap  may  occur,  best  from  below  upward,  and  in  the  first  measure. 
In  the  midst  of  a  movement,  however,  octaves  in  the  bass  should  be 
employed  very  sparingly,  and  only  in  exceptional  situations. 


Beginning. 


Close. 


55. 


Se 


^g- 


^ 


7          7         — 


§  6.  The  contrapuntal  movement  seldom  or  never  extends  into  the 
last  measure ;  in  the  first  it  may  also  be  omitted,  and  the  bass  may, 
occasionally,  not  enter  till  the  second  measure. 


56. 


COUNTERPOINT  IN  BASS. 


17 


No  other  passing-note  besides  the  seventh  on  the  weak  beat,  pro- 
gressing stepwise  from  the  octave  of  the  root,  and  proceeding  down- 
ward, is  permissible.  The  leading  of  the  bass  in  57  a  is  wholly  bad  ; 
that  at  57  b  is  good. 


a.  bad. 


6.  good. 


$—&- 


57. 


Xl           ^ 

<^ 

O' 

a         i 

icn     " 

& 

^ 

—  (S>  

§*- 

2 

2 

,         ;   2 

6 
5               7 

/<•};  1  ^  

F*             ^ 

-^             j 

—  !  1  — 

1 

S2  .  1  

-1  1  

-^  1 

As  the  only  diatonic  progression  accorded  to  the  bass  is  the  sev- 
enth mentioned  above,  and  as  this  part  must  generally  move  by  leaps, 
we  may,  in  special  cases,  write  two  chords  to  one  of  the  cantus  firmus 
under  proper  conditions,  in  case  this  procedure  permits  the  bass  to 
progress  diatonically  ;  provided,  that  the  harmonic  connection  is  clear, 
natural,  and  easily  understood,  as  is  shown  in  Ex.  58  at  N.B. 


N.B. 


58. 


§7.  With  the  triad  on  the  1st  degree  in  minor,  the  seventh  in  the 
bass,  following  the  root  of  the  triad,  must  always  be,  in  conformity 
with  the  melodic  minor  scale,  the  natural  (i.  e.,  not  raised)  7th  de- 
gree of  the  minor  scale. 


18 


UNEQUAL   COUNTERPOINT. 


59. 


In  the  first  measure  of  Ex.  59,  the  leading  of  the  bass  can  be  no 
other  than  A-G-JF,  etc.  The  7th  degree  of  the  minor  scale  is,  there- 
fore, not  raised  in  this  case. 

Retarded  consecutive  octaves,  such  as  are  found  in  sequence- 
form  on  the  weak  beat  in  several  measures  of  Ex.  60,  are  not  per- 
missible, more  especially  as  the  monotonous  and  stiff  leading  of  the 
outer  parts  is  not  good. 


bad. 


6O. 


Retarded  consecutive  octaves  between  the  first  tone  (on  the  strong 
beat)  of  one  measure  to  the  second  tone  (on  the  weak  beat)  of  the 
next,  are,  however,  entirely  neutralized  in  effect  by  the  two  interposed 
tones,  and  therefore  allowable. 

good. 


61. 


/k(*  —  °-  — 

—  &  — 

-°-       \ 

vsly              ^f~ 

~J 

Z 

8                                               8 

7S&  1        1 

j0 

^5 

L«ii|L_^  C 

-1  1  

i  

An  isolated  pair  of  consecutive  octaves  from  one  weak  beat  to  the 
next  weak  beat,  is  allowable ;  but  such  octaves  must  not  appear  in 
several  successive  measures,  as  in  Ex.  60.  No  fault  can  be  found 
with  Ex.  62 ;  Ex.  63  has  the  same  beginning,  but  the  further  pro- 
gression is  bad. 


COUNTERPOINT  IN  BASS. 
Quite  correct 


62. 


L — <s>-\ 


32\ 


19 


Not  good. 


63. 


/L  (\*    ^ 

—  ^  

^- 

^/^ 

-h»  —  | 

ffT\  1  y       :T 

—  . 

S3 

*^r 

1       X=5 

' 

^ 

&* 

T      g              | 

«T 

6                        6 
4                        57 

/A^\«    - 

^- 

^5 

^. 

22 

£M^-^- 

!           r9 

-f  

§  8.  We  shall  now  give  the  student  some  illustrations  of  a  counter- 
point of  two  notes  in  the  bass  against  one  in  the  cantus  firmus,  which 
latter  may  be  set  either  in  the  soprano,  the  alto,  or  the  tenor. 


The  Cantus  Firmus  is  in  the  Soprano. 


64. 


7  (2) 


6 

5  7 


•«• 1 1- 


S3 

tgj^1—  a  

—  

escs 

^i  

?5  

o- 

-<&-                      -i$- 

-<S>-                       -S- 

-« 

j.                         » 

7                           2 

67                           26 

2 

>^A.            —  ^ 

| 

] 

1 

t     L 

~*"           —  i 

j 

,  ^.  

™  3  —  1 

1    •       f- 

g»    • 

2^ 

* 

(51           1 

20 


UNEQUAL    COUNTERPOINT. 


N.B.* 


At  N.  B.  1  the  seventh  .F  in  the  alto  must  be  led  upward,  because 
the  passing  seventh  F  in  the  bass  has  to  progress  downward.  [The 
chord  on  the  weak  beat  of  measure  5  is  considered  to  be  a  chord  of 
the  2d  (though  it  is  really  a  6-4  chord)  because  of  the  impression 
made  by  the  fundamental  G  in  the  bass,  on  the  strong  beat.  TR.] 
In  like  manner,  at  N.  B.  2,  the  seventh  F  in  the  alto  must  go  upward, 
because  the  bass  leaps  to  the  proper  tone  of  resolution,  E.  (See  Man- 
ual of  Harmony,  §45.)  At  N.  B.  3,  the  retarded  consecutive  octaves 
on  the  weak  beat,  between  the  outer  parts,  are  permitted.  (See  ~Ex..  62.) 

The  next  counterpoint  is  written  to  the  cantus  firmus  given  in 
Ex.  44,  the  c.  f.  in  the  alto. 


This  example  requires  no  further  explanation. 

The  next  is  a  working-out  of  the  cantus  firmus  given  in  No.  48, 
set  in  the  tenor,  with  a  counterpoint  of  two  notes  against  one  in  the 
cantus  firmus. 


COUNTERPOINT  IN  BASS. 


21 


66. 


C.  f.  in 
Teuor. 


127 


4 
3 

-&- 


-^ 


6 
-I?-    7       jO- 


"f 


5^ 


1 — f- 


-^ — c 


tt= 


g=E= 


r 


No.  65  might  also  begin  as  follows : 


67. 


m 


In  order  to  furnish  the  student  with  as  much  practical  guidance 
as  possible,  we  add  several  workings-out  of  the  cantus  firmus  given 
below  ;  only  the  last  contains  a  modulation. 


68. 


22 


UNEQUAL  COUNTERPOINT. 


69. 


3tE£ 


6 

5          7 


-t: 


s 

n 

—  19  

-7575  1 

^  

V 

tn 

—  

o 

—  , 

*J         -&- 

4 
3              7 

7-r;  1  1 

-G>- 

Z 

-G>- 

2 

& 

7 

feifc—  d  ^~ 

—  1  H 

1  ^~ 

~             ^ 

Vta^    2 

&>             ^j 

^ 

\ 

fS            \ 

70. 


^K  (r       ^ 

1  —  &  

es 

'" 

|0)  V^  —  fig  

—&  

—  15>  —  •  

—  &—.  

—  ^  —   _ 

-&-          -&- 

27                                                                        7 

/WA«    1 

. 

a 

t-*r 

I™^«^l»         _ 

f^               /*^? 

x^ 

_. 

V^i)^  S?  — 

1  

—  —  s*— 

-^  1  

-^  —  I  

2 

f 

^ 

&  

f^f 

h^M 

6 
5              7 

-&- 

-^  

-&- 

~&~ 

-S- 

JU!  ^_ 

_E  (S_ 

fy 

f? 

^  ^  

&            ~P 

^  

MODEL  EXAMPLES. 


23 


71. 


— z? — 


«SE 


-t: 


-fj       * 


'--*• 

mf\\.           £S 

_^^ 

^-^ 

'^V- 

^/^ 

"^^  

^'&~ 

:^ 

7 

(m\*                i 

-^ 

^5 

1 

]9J'     3 

^5                   -^ 

^ 

r"*^            _^ 

j                                        ] 

SS     "^         2 

I                       1 

i              [^ 

a 

72. 


-&- 

ffiE 


-&-  -<&- 

2  7 


=t=: 


yf- 

—  <5x  — 

*•* 

*•*     i 

0 

f^^ 

^22 

^ 

1 

U         ^ 

6 
5             7 

-<S>- 

-&- 

9 

7 

<a 

-&>- 

^-t- 

(jg  j  1~ 

-&     ^ 

5     ^^ 

-&•  ^~ 
—  j  —  —  —  |  — 

1 

\  &  ^j  — 

1-^  \~ 

1  — 

1 

73. 


=t= 


24 


UNEQUAL    COUNTERPOINT. 
N.B. 


i?r\        /o 

o 
*t/r/ 

& 

f^> 

&   - 

=    1 

HZ 

3* 

19   ••         ^ 

rj             --gy 

SSr-i—A-n 

-sr 
2 

-&-^  

-G>- 

—  - 

-V        \ 

-&• 

(ftfc  ^  

—  ?5  ^  — 

—  <9  $9  — 

-<*  1- 

^  &— 

-+  g 

-^  *- 

-1  EE 

! 

A  chromatic  passing-note,  as  at  N.  B.  in  Ex.  73,  may  occasionally 
be  employed ;  such  a  note  then  assumes  the  character  of  an  altered 
tone  progressing  upward  from  the  natural  tone.  This  does  not  give 
a  true  modulatory  effect.  The  beginning  of  the  preceding  cantus 
firmus  may,  therefore,  also  take  the  following  accompaniment : 


74. 


But  several  such  chromatic  progressions  must  never  follow  each 
other  in  succession,  for  then  the  leading  of  the  counterpoint  would 
take  on  a  "whimpering"  (heulende)  expression,  as  the  old  musicians 
put  it.  The  essential  characteristic  of  genuine  counterpoint  is  dia- 
tonic melody.  The  following  illustration  is,  therefore,  wholly  to  be 
condemned.  (Compare  Man.  of  Harm.,  §57,  Exs.  301  and  302.) 


75. 


The  seventh  on  the  weak  beat  in  the  alto,  in  Ex.  73,  measure  be- 
fore the  last,  is  allowable  in  any  part  at  the  close. 

§8.  The  student  may  now  work  out  some  exercises,  setting  two 
notes  in  the  bass  against  one  in  the  cantus  firmus.  He  should  take, 
for  the  soprano,  any  appropriate  cantus  firmus  found  in  the  Examples 
from  No.  29  to  36 ;  for  the  alto  and  tenor,  from  No.  40  to  48.  But 


COUNTERPOINT  IN  THE  BASS. 


25 


now  in  this  work  in  unequal  counterpoint,  the  student  ought  not  to 
rely  in  the  least  on  his  former  work  with  the  same  cantus  firmus  in 
equal  counterpoint,  or  on  any  earlier  harmonizations.  By  so  doing  he 
would  not  facilitate  matters,  but  only  render  them  more  difficult.  If 
he  were  always  to  retain  the  same  harmony,  it  would  be  a  purely 
mechanical  process  to  insert  a  second  half-note  upon  each  weak  beat 
in  the  bass,  and  one  wholly  reprehensible  because  wholly  inartistic. 
And  he  would  also  speedily  perceive,  that  methods  which  were  quite 
fit  and  proper  for  working  out  exercises  in  equal  counterpoint,  are 
very  frequently  neither  fit  nor  proper  for  work  in  unequal  counter- 
point. 

On  attentively  examining  Exs.  64,  65,  66,  68,  69,  70,  71,  72,  and 
73,  no  one  can  fail  to  notice  that,  in  the  counterpoint  of  the  bass,  the 
fifth  of  a  triad,  falling  on  the  weak  beat,  was  employed  only  very 
rarely  (Exs.  65  and  71).  But  such  "after-striking"  fifths  on  the 
weak  beat  are  by  no  means  forbidden.  The  next  contrapuntal  illus- 
tration is  quite  correct,  although  the  after-striking  fifths  of  the  triads 
on  the  1st  and  4th  degrees  are  introduced. 


76. 


L/  ,     i 

1 

^\i?(|y  — 

ts 

'  ^  

f? 



~^~l 

v-'y 

& 

& 

/- 

*s*5> 

^ 

^                1 

tr 

x^"" 

**. 

-&-^ 

^ 

-<s*- 

6»v  , 

i 

PS  /* 

-^ 

1 

S^ 

| 

5Z5IB 

& 

2 

& 

-^. 

& 

Consequently,  such  after-striking  fifths  are  not  forbidden  in  the 
case  of  triads,  and  still  less  in  seventh-chords,  in  which  they  form  a 
chord  of  the  third  and  fourth  on  the  second  beat.  But  we  must 
frankly  admit,  that  the  frequent  use  of  the  after-striking  fifth,  in  the 
case  of  triads,  renders  the  effect  of  the  counterpoint  in  the  bass  rather 
feeble,  lame,  and  awkward.  We  therefore  warn  the  student  against 
a  too  frequent  employment  of  this  interval.  For  the  above  reason, 
Ex.  77  cannot  be  praised,  although  it  does  not  transgress  any  of  the 
rules  already  given. 


77. 


26 


UNEQUAL    COUNTERPOINT. 


These  after-striking  fifths  of  triads,  marked  *,  may  be  readily 
avoided,  as  we  show  in  Ex.  78. 


78. 


In  closing  this  chapter  we  desire  to  call  attention  to  the  fact,  that 
it  is  not  advisable  to  keep  the  student  too  long  at  work  on  these  (by 
no  means  easy)  exercises.  For,  in  practice,  mixed  counterpoint  in 
several  parts  at  once  is  usually  employed.  Moreover,  the  same  and 
similar  exercises  will  be  repeated  in  the  three-part  and  two-part 
exercises.  In  instrumental  and  vocal  instruction,  the  student  is  not 
kept  at  work  on  one  and  the  same  etude  until  he  can  perform  it  per- 
fectly. Going  on  to  other  new  exercises,  he  gradually  learns  to 
master  the  earlier  difficulties  with  increased  skill.  As  soon  as  the 
student  has  acquired  some  little  dexterity  in  the  writing  of  a  contra- 
puntal bass  in  two  notes,  the  following  chapter  should  be  taken  up. 


CHAPTER    III. 
The  Counterpoint  in  the  Higher  Parts. 

§  10.  When  it  is  required  to  write,  in  the  counterpoint  of  one  of 
the  higher  parts,  two  notes  against  one  in  the  cantus  firmus,  eight 
different  kinds  of  progression  are  allowed,  namely : 

1.  The  leap  of  a  tone  to  another  tone  belonging  to  the  same 

chord. 

2.  Suspension. 

3.  The  tying-over  of  any  chord-tone  to  the  same  tone  in  the 

following  chord  in  the  next  measure. 

4.  Any  "after-striking"  seventh  on  the  weak  beat,  descending 

from  the  octave  of  a  root,  and  immediately  progressing 
downward. 

5.  The  leap  to  the  root  of  a  seventh-chord,  when  the  tones 

forming  a  triad  in  the  latter  were  already  sounded  on  the 
strong  beat. 


COUNTERPOINT  IN  THE  HIGHER  PARTS. 


27 


6.  The  leap  to  the  dominant  seventh,  and  to  any  other  minor 

and  diminished  seventh,  where  this  progression  serves  as 
a  fitting  preparation  for  the  ensuing  (suspended)  minor  or 
diminished  seventh.  A  leap  to  a  major  seventh  should 
always  be  avoided  ;  consequently,  a  suspension  can  be 
prepared  by  a  major  seventh  only  in  exceptional  cases  and 
under  special  conditions,  as,  for  instance,  in  a  sequence 
of  suspensions.  (See  Ex.  85  6,  measure  3.) 

7.  Suspension  before  the  root  of  any  fundamental  triad  in  the 

key.  even  when  this  root  is  already  present,  sounding  to- 
gether with  the  suspended  tone,  in  an  inner  part.  The 
root  must,  however,  be  at  an  interval  of  a  ninth  from  the 
suspension,  and  below  it.  (See  Manual  of  Harmony,  §57, 
Ex.  257  6,  c,  and  d.) 

8.  A  suspension   prepared   by  an   after-striking  seventh  pro- 

gressing stepwise  from  the  root  of  the  triad  on  the  strong 
beat,  when  said  suspension  is  in  the  midst  of  three  or  more 
suspensions  or  tied  harmonies,  which  all  together  form  a 
sort  of  chain  or  sequence. 

NOTE.  —  The  reason  why  sevenths  cannot  be  used  in  preparing  suspensions,  except- 
ing in  the  cases  enumerated  under  6  and  8  above,  is  easy  of  comprehension.  The 
sevenths  themselves  are  dissonances,  and,  as  such,  require  resolution.  Only  the  leap 
to  the  minor  or  diminished  seventh  gives  these  intervals  sufficient  force  and  momentum 
(so  to  speak)  to  support  and  prolong  the  following  dissonance  of  the  suspension.  The 
cases  mentioned  under  6  and  8  are  referable  to  the  peculiar  characteristics  of  the 
sequence. 

Illustrations  of  these  Eight  Rules. 


(1.)  The  leap. 


79. 


(2.)  The  suspension. 


SO. 


28  UNEQUAL   COUNTERPOINT. 

(3.)  Tied  notes. 

-j ^ 


81. 


M — z? 


m 


(4.)  After-striking  seventh. 

J— 4-, .-- J U 


82  a. 


1  -4- 


87 


87 


a. inz 


Even  progressions  like  those  under  82  b  may  be  written  without 
hesitation. 


826. 


6         5 


6        5 


An  after-striking  fifth,  following  a  chord  of  the  sixth,  is  to  be 
conceived  as  the  seventh  of  an  incomplete  chord  of  the  fifth  and  sixth, 
the  root  of  the  fundamental  seventh-chord  having  been  heard  just 
before  in  the  same  part. 


(5.)  After-  striking  root  of  seventh-chord. 


83. 


JLn-^-L 


C:  IV      II, 


VT 


VI        IV. 


COUNTERPOINT  IN  SOPRANO. 


29 


This  kind  of  progression  will  be  used  but  seldom,  and,  as  a  rule, 
in  the  manner  shown  in  the  four  measures  of  No.  83.  In  such  cases, 
the  seventh-chord  on  the  weak  beat  must  always  appear  as  a  complete 
chord  of  the  fifth  and  sixth  with  all  its  intervals.  Progressions  like 
those  given  under  No.  84,  are  not  to  be  commended,  though  in  prac- 
tice they  may  perhaps  be  occasionally  employed. 


Not  good 


Not  good. 


Not  good. 


84. 


C:  IV        ii7  vn°7      VT  in         IT 

In  Ex.  84  a,  the  chord  of  the  fifth  and  sixth  sounds  empty,  its 
third  (the  fifth  of  the  fundamental  chord)  being  omitted.  At  6,  the 
sixth  (the  third  of  the  fundmental  chord)  of  the  chord  of  the  third 
fourth,  and  sixth  is  wanting.  At  c,  the  root  of  the  seventh-chord  on 
the  1st  degree  enters  by  a  step,  not  by  a  leap  ;  consequently,  the  effect 
is  weak,  although  the  chord  of  the  fifth  and  sixth  appears  complete, 
with  all  its  intervals,  on  the  second  beat. 

(6.)  The  leap  to  the  minor  and  diminished  seventh  in  order  to 
prepare  a  suspension ;  and  the  suspension  prepared,  in  a  sequence, 
by  a  major  seventh. 


85. 


C:  II         II7  V. 


a:  VII0     VII c 


30 


UNEQUAL   COUNTERPOINT. 


Always  avoid  taking  the  major  seventh  by  a  leap ;  consequently, 
it  cannot  be  used,  like  the  minor  or  diminished  seventh,  to  prepare  a 
suspension.  Ex.  85  6,  measure  3,  shows  how  the  major  seventh,  en- 
tering by  a  step  and  on  the  weak  beat  after  the  octave,  may  be  used 
to  prepare  a  suspension  in  the  midst  of  a  succession  (sequence)  of 
suspensions.  In  a  seventh -chord  with  altered  fifth,  to  be  sure,  the 
dissonance  of  the  major  seventh  is  not  so  harsh  in  effect ;  but  then  no 
suspension  is  possible,  because  the  altered  fifth  must  always  be  led 
upward  (see  Man.  of  Harm.,  §48,  p.  119*),  and  would,  therefore,  take 
the  tone  of  resolution  of  the  suspension  before  the  latter  was  resolved. 


When  two  contrapuntal  parts  are  set  in  half -notes  against  whole 
notes  in  the  cantus  finnus,  it  would  be  possible  to  lead  them  thus : 


J 


We  subjoin  the  working-out  of  cantus  finnus  No.  100  in  sequence- 
form. 


(100.) 


^q       I*-R-I — -3=F;, 

-^ z£-  —  & — gH— 

~~^  I       <*   —&-\— 


r  -  1  -  &^ 


H 


*  The  page-numbers  refer  to  the  Revised  English  Edition  of  Jadassohn's  "Man.  of 
Harm.",  published  by  G.  Schirmer,  New  York. 


COUNTERPOINT  IN  SOPRANO. 


31 


-& 75*- 


— <g — 
-zr 


— IV        I 

us? — I 


-?£ 


N.B. 


N.B. — Compare  Manual  of  Harmony,  §  53,  p.  152,  Ex.  257  c. 


(7.)  Suspension  before  the  root  of  any  fundamental  triad,  even 
when  the  tone  of  resolution  of  the  suspension  is  already  present  in  an 
inner  part.  (Study  the  reason  for  this,  and  the  examples  in  notes,  in 
Manual  of  Harmony,  §53,  Ex.  257  6,  c,  and  d.) 


Suspension  before  the  root  of  the  tonic  triad. 


86.  / 


54 
226 


76  —          7       — 

5—54  43 


C:   I 


«T 


Suspension  before  the  root  of  the  dominant  triad. 

N.B. 


87.  ( 


-<5^  I          lor  -&-  -TST 

9    8                 /  7     — 

.4    3^. V7  —  „ ^7/6, ^8     1, ^4     3  66 


iZ I (3. ^ &. 


V,          I 


32 


UNEQUAL    COUNTERPOINT. 


Suspension  before  the  root  of  the  subdominant  triad. 


88. 


fl  Jq 

-  J  t: 

i—  ^  r~ 

u 
^-1  i 

L- 
-«•-    ^ 

-     1         1 
^      ^!- 

x    1       U 

gj  -4 

E5EBE 

_  , 

^^ 

^^  i 

<s 

o 

;   ^ 

f^i 

2B 

a 

fTj 

& 

£2 

-<£»       ' 

">  

7       6 

^  ^  — 

7 

s     ~^  — 
6        — 
5         4 
3       — 

s 

7       6 

7       6 

7      
6       5 

{^\*    I 

<v 

1 

^-, 

1 

•* 

(»...  .- 

C:    I 


IV 


(8.)  Suspension  prepared  by  the  after-striking  dominant  seventh, 
progressing  stepwise. 

An  example  of  this  preparation  may  be  seen  at  N.B.  in  Ex.  87, 
measures  5  to  6. 

§11.  We  shall  now  begin  our  exercises  with  the  counterpoint  in 
the  soprano  to  a  cantus  firmus  in  the  bass  ;  exhibiting  the  employment 
of  all  eight  kinds  of  progression  in  one  example  in  notes.  To  add  to 
its  perspicuity,  each  kind  of  progression  is  numbered,  when  it  first 
occurs,  in  conformity  with  the  scheme  presented  above. 


2. 


3. 


up. 

89.  < 

C.f. 

/L  W         •        & 

o       ^' 

& 

&*                  ^            J 

\r\\  \.\j      *••,  ~~> 

'  ^r-^ 

Ijny   '            ^ 

^^ 

2                                   J 

"         '        "         *        * 

y^^«    1 

fp 

I 

EZjZB 

/^ 

£} 

»                                  J 

^-^V^  —  ^  

^  

-^  1 

5. 


s. 


fr\     ^       '& 

^  1 

&  -*** 

—  '  —  r 

_^  ^_ 

-A 

&            & 

ey      .3 

^  J  ^ 

f      i 

tr~Tg. 

fm~\' 

-ST 

cs 

•^ 

<s 

-&- 

o 

&-  & 

i  —  ^  —  i 

& 

sy 

-G>- 

o         1 

P   1        I 

S3 

^ 

M 

COUNTERPOINT  IN  SOPRANO. 


33 


The  student  must  not  assume,  however,  that  he  is  obliged  to 
employ  all  these  eight  different  styles  of  progression  in  each  exercise. 
On  the  contrary,  he  ought  to  use  only  the  most  usual  kinds,  which  are 
numbered,  respectively,  2,  1,  4,  6,  3.  The  succession  given  here  is 
intended  to  express  our  opinion  of  the  order  of  precedence.  Thus,  we 
consider  the  suspension  to  be  the  best  means  for  carrying  on  the 
progression  of  the  counterpoint  in  two  notes  ;  tied  notes,  on  the  other 
hand  (especially  such  used  in  several  successive  measures),  should  be 
most  sparingly  employed.  More  than  two  successive  leaps  are  not 
in  conformity  with  the  diatonically  melodic  nature  of  counterpoint. 
On  this  account,  the  following  counterpoint  is  not  to  be  commended, 
though  it  does  not  transgress  any  of  the  given  rules. 


Not  good,  on  account  of  too  many  leaps. 


Cp. 

9O. 

c.  f. 


As  a  general  rule,  it  is  best  to  employ  in  alternation  the  ordinary 
kinds  of  progression  as  their  use  appears  convenient  and  appropriate ; 
and  to  use  the  less  common  ones  (under  5,  7,  and  8)  only  where  they 
seem  peculiarly  adapted  for  the  carrying-out  of  the  contrapuntal  pro- 
gression. Suspensions  alone  may  be  used  for  several  successive 
measures  ;  but  do  not  insist  on  overloading  the  work  with  suspensions. 
Taste  and  sound  musicianship  must  decide,  in  each  case,  what  kind 
of  progression  is  to  be  employed.  The  best  test  of  the  excellence  of 
any  counterpoint,  is  the  degree  of  its  difficulty  for  singing.  Of  course, 
a  healthy,  natural  harmonic  progression  is  a  sine  qua  nan.  A  se- 
quence-like leading  of  the  contrapuntal  part  must  not  continue  through 
more  than  three  successive  measures. 


Cp. 

91. 

c.  f. 


H        ^ 

s    s 

^ 

<> 

UNEQUAL    COUNTERPOINT. 


F=ffF= 

&        itai 


ii 


The  first  four,  or  even  six,  measures  in  Ex.  91  are  not  bad ;  but 
the  continuation  in  similar  style  grows  monotonous.  Under  certain 
conditions,  even  a  sequence- like  ascent  of  the  counterpoint  at  the 
beginning  of  a  movement  has  a  very  good  effect ;  but  the  repetition 
of  the  sequence  or  the  sequence-like  progression  must  not  overstep 
three  measures  at  most.  The  beginning  of  Ex.  92  is,  therefore,  good, 
as  were  the  first  measures  in  Ex.  91. 


Cp. 

92. 

c.  f. 


Where  the  cantus  firmus  itself  has  a  progression  in  regular 
cadence-form,  it  is  best  to  lead  the  other  parts  likewise,  and  also  the 
counterpoint,  in  sequence-like  progression  ;  e.  g., 


93. 


c.  f. 


XL   ir               E 

*~ 

H                                    

fm    vp      ^J  /-t; 

£•** 

^X                        .^rj 

r             —  -S- 

^X 

^^, 

* 

-&~ 

/^~\c         , 

S^j 

1 

[CJ«  /U 

" 

W^  ID 

or: 


CANTUS  FIRM  US  IN  ALTO. 
Or  as  in  the  next  example: 


94. 


c.  f. 


35 


XL    f*     ^^ 

fm  IE 

lw" 

f^1                                            1         j*T3                    ^^ 

r" 

S3 

—  .,                                           |         'jf' 

-&- 

(£)'  /It  

ffi  

_  

Wi_i^  — 

JJL=^  4^= 

3  —  =M 

p=t=  —  ^^ 

=Xc-l  1  1 

—  ^^  .  ,            j  

* 

^ 

25 

—G>  • 

/j^V             ^ 

1    " 

o. 

(2               \ 

l£^7  

__  

—a.  

§  12.  Here  follow  a  few  more  illustrations  of  a  counterpoint  in  the 
soprano  to  a  cantus  firmus  in  the  alto  or  tenor. 

In  Ex.  95,  the  cantus  firmus  is  in  the  alto. 


c.  f. 
95.  < 

/L  -4«   -2 

2       32 

&     \    &        2 

fm    !Q    E. 

<^                        ^,       ^         <C? 

B22 

^,3 

1      ^                 1     -^ 

ss               \ 

^T               &    "             ^                  es                                        '<* 

—&  1 

f^\*vt    i       ^ 

sp 

'-*"                       ^^ 

& 

^Il^u_ 

ss 

-»  H 

-                & 

^p 

^r~j          ^^ 

& 

&            \ 

'•* 

*-^ 

& 

&             \ 

*} 

•  — 



S3 

-G>- 

fij 

-G>- 

jd. 

^2. 

(m\^. 

1 

WJ3r 

sy 

^f~ 

SS±:  *= 

& 

*-^ 

UNEQUAL    COUNTERPOINT. 


In  Ex.  96,  the  cantus  firmus  is  in  the  Tenor. 


Cp. 

96. 
C.£ 

A                                              !  1                    1 

j           J          J              »             , 

I 

f-     \        \         J 

<rj              «              «>       - 

•57  3            1 

r   /*       '        & 

& 

ex            I 

)•  H'     i^-c1 

G>  

gy~  . 

—  ^  

—  «•             H 

-&                ^ 

p.                      ^SL                     ^! 

fa)'  /|» 

—  s>  — 

_  

W'  lp        a 

—  5>  

J 

j           | 

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^  '      J 

L'         *^               -^ 

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0         1 

£^ 

£"^ 

I 

l/^k                     ^^ 

CS                  jr- 

^    **fS 

__ 

^      "I 

\^-]/                ^2 

f^>                ^"^ 

^ 

^r 

&        \ 

-f5>- 

-&- 

-&- 

{^\* 

Sp 

f^j 

1 

fc^  ^  

/•^ 

~ 

The  student  has  now  to  write  a  counterpoint  of  two  notes,  in  the 
soprano,  to  each  cantus  firmus  given  below  for  bass,  alto,  and  tenor. 
In  case  more  or  different  exercises  should  be  desired,  the  cantus  firmus 
in  any  of  the  preceding  examples  may  be  provided  with  a  counter- 
point in  the  soprano. 


Exercises. 


97. 


NOTE. — Compare  the  given  bass,  No.  97,  with  Ex.  96. 


98. 


99. 


\00. 


CANTUS  FIRM  US  IN  THE  INNER  PARTS. 


37 


1O1. 


_<2 6>-  ^- —  -^ & <2 __|_^rp2 


-& &— 


CL^'i  Zffi 

f^ 

__ 

•  r^^b  sP 

f^ 

*-^ 

5? 

h       i/     i 

^f 

j^ 

104.  F<B- 


105. 


1O6. 


Cantus  firmus  for  Alto. 
-^-H*-     "*" 


1 


107. 


. 

108. 


1 


Cantus  firmus  for  Tenor. 


1O9. 


1 


no. 


For  the  working-out  of  cantus  firmus  108  we  add  a  few  hints. 
The  cantus  firmus  is  set  in  the  alto ;  the  counterpoint  in  the  soprano 


38 


UNEQUAL    COUNTERPOINT. 


should  have  two  half-notes  against  each  whole  note  in  the  cantus 

iirniiiH : 

:fc=J^     ^  T^^S--*'-?^— abEJ  N 
c  f . 

lOSa. 


fpl\  WT-j  ^ 

& 

-                          -,             *—\ 

VJ)      1 

1     » 

1     2              I 

tT~ 

^ 

/^\*  i 

<£?(p  ^  — 

S3                                  ^ 

<S?  

N.B.— Compare  Manual  of  Harmony,  §53,  p.  152,  Ex.  2576. 


yr-    J      o" 

~*s3          ^.} 

jg 

'-*"            |      *^ 

^^y                  ^-1 

H      1 

*-*^ 

1 

^^ 

IQ) 

s'j 

.dPl 

1     - 

t^      -(&- 

?                      **                 -<S>- 

frj-:—  »  

S3 

^rf? 

S3 

f2 

^5 

^,. 

<~s 

*** 

^ 

~- 

es 

^H I I 

=1=33 

,0 • 


The  covered  fifths  between 
tenor  and  bass  are  permitted  on 
account  of  contrary  motion  in 
the  soprano. 


C.  f. 


1086. 


JLyfr           ^                    £/* 

»sH  —  ^q 

—  '  —  25*~1 

-^--&— 

—A  —  &—^-& 

^*  

- 

-&- 

-*  1  1 
|—?5  V—&  3 

LJlt-^— 



&                   ^           ~n 

CANTUS  FIRM  US  IN  THE  INNER  PARTS. 


39 


—I. 


C.f. 
1O8  c.  < 


?£_ 


1  I 


^^^^ 


40 


UNEQUAL   COUNTERPOINT. 


C.  f.   \ 

/^v^tr  —  a  — 

^tf 

L^           & 

2 

-&—4-A 

S3 

•^ 

j 

y 

U                                                                                      -&- 

1O8  d.  < 

/ 

-<y-                            -«s>- 

fm^'    i 

'*£-. 

^Sln 

f2                         • 

—  &  

^  

—  ^e  

_«2  J 

m 


-    ! 

u 

-       \               \ 

Lr                   I                    !' 

&         1 

I         -, 

, 

1 

xT          j         <^ 

1  **— 

£J 

-^  1 

\SiT  ^5  

&  — 

&  7$  

1 

0 

-&- 

^^  ^  

(3 

a 

C.  f.  I 
\O8e.  < 

Jr  "  t      /J 

J 

-«.  1—  a:  —  ^j—j 

—  9  — 

a 

—  (5*  1  1 

«/                                                                                                                                     -(51- 

or: 

/^A« 

S3                            /«^ 

DM&ZS 

%  —  '\1^             <^ 

—  fz  

s? 

«                     (S? 

Vl                         ^X                        ^- 

-   -,5?  •    p  ^ 

1 

/m    '                * 

1                          '^ 

IMJ         « 

/*v  /o 

• 

0 

a 

&- 

^5  

rfO  

75-  

COUNTERPOINT  IN   THE  INNER  PARTS. 


41 


c.f. 
108/. 


fi  /*"v              !-^T—     1 

| 

1 

•^ 

J                  1  — 

•»-     | 

^^x              —  - 

<^ 

r  \ 

2 

la 

-j       2 

S            2 

& 

& 

& 

1            1 

I£J-       ^ 

_ 

SE 

^            1 

^"""'                                              <!V 

& 

-^  1 

§  13.  For  the  leading  of  a  counterpoint  in  the  alto  or  tenor,  the 
rules  given  above  (§10)  are  applicable.  The  seventh  kind  of  pro- 
gression, however,  can  be  employed  only  in  the  alto.  ~Ex.  Ill  ex- 
hibits this  case  twice,  in  the  measures  marked  N.B. 


Cantus  Firmus  in  the  Soprano. 

N.B. 


N.B. 


Cp. 

111. 


The  contrapuntal  progression  in  one  inner  part  alone,  is,  however, 
much  harder  to  write  than  in  an  outer  part ;  the  kinds  of  progression 
will  generally  be  limited  to  Nos.  1,  2,  3,  4  (the  leap,  the  suspension, 
the  tied  note,  and  the  after-striking  seventh).  Occasionally,  too,  we 
cannot  help  dividing  the  two  inner  parts  by  an  interval  exceeding  an 
octave ;  but  this  must  not  continue  too  long,  otherwise  the  harmony 
will  sound  empty.  The  following  working-out  of  cantus  firmus  No. 
Ill  is,  for  this  reason,  not  good. 


UNEQUAL    COUNTERPOINT. 


Bad,  on  account  of  too  wide  interval  between  inner  parts. 


C.  f. 

Cp. 

112. 


&—&- 


By  way  of  illustration,  we  now  give  a  working-out  of  a  cantus 
finnus,  set  in  an  inner  part,  in  six  different  examples. 


Alto, 
c.  f. 

Cp. 

113. 


The  Cantus  Firmus  is  in  the  Soprano,  the  Counterpoint  in  the 


XL  4    /I*       m 

«          I 

HP 

v^y                            f3 

f^                -_ 

i  — 

^      !   •*- 

"*1      ?    ' 

?        1- 

n    r 

0         \ 

1         ' 

f                f      N^ 

/^A«    —     i           ^-j 

- 

^_ 

"1 

E2a  7/»     ®" 

2J 

2, 

^-, 

^5 

N^fo    \U       « 

--) 

cs 

2 

1 

K  T  

& 

& 

% 

& 

1  1 

—  &  —  i 

Vs|^             i^             fS1 

S3               \        — 

~^     \ 

\                      S3 

<^s                 ^^ 

i 

tJ  ^  ^         n  ^  r        i        i                i        i  v  ^  i        f      ^ 
1 

f»}'  n      '% 

S6 

• 

*wli 

sp 

^ 

The  Cantus  Firmus  is  in  the  Soprano,  the  Counterpoint  in  the 
Tenor. 


U.  I. 

114.    < 

Cp.      ) 

frt\  ^    VI  y      ^^ 

cs 

'  <* 

V'ly                   ^^ 

^^ 

^/ 

S2 

5T 

i                   |                                                       1    ^~V     1                  I    ^^    |                  1                   I      -d- 

^          _J'*~V  -J                                  O          O          -J         _^.J             I  ^^\J 
—       ^         ^            i            |                               -e*-      -e^-       ^         ^ 

^•j 

11 

©M^ 

^Q  

—&  

'  —  ^  — 

COUNTERPOINT  IN  THE  INNER  PARTS. 


43 


ffK"  —  ^  

—  (2  

S3Z 

^? 

c*' 

^^ 

^  A—  A   j_,    _,    j  2  A  ^  ,, 

(m)'  K      f> 

\&/h 

^ 

cs 

fy 

The  Cantus  Firmus  is  in  the  Tenor,  the  Counterpoint  in  the 


Alto. 


Cp. 

\\5. 

c.  f. 


g-,  [— |-^;=^t    '        ^ 


-^- 


,^p_ 


Or  these  four  measures. 


The  Cantus  Firmus  is  in  the  Alto,  transposed  into  ^7^  major ; 
the  Counterpoint  in  the  Tenor. 


c.  f. 
116. 

Cp. 


j<7_ 


44 


UNEQUAL   COUNTERPOINT. 


Or  the  following  three 
closing  measures. 

>K~tet  —  ?  

S3 



—  (5"  •  —  - 

_  1 

(en 

5* 

^> 

1           ^ 

^/ 

•^    :                           ___^_Jfi1_^ 

JL             1^1              , 

/^A«      U 

1 

'•^ 

-S      _i 

(£>LV 

—  <9  — 

—  X3  

^            1      « 

—  ^  

^" 

The  Cantus  Firmus  is  in  the  Bass,  transposed  into  G  major ;  the 
Counterpoint  in  the  Alto. 


/^ 

*r~         ^~ 

s^ 

-,£,  

—  j 

J\                 S3 

Cp. 

^iy          '                           <** 

^*^            ^S 

—  "  : 

2S 

T  fd 

tj                   Zs           1    -^^                                               I                  1 

1                                   '                                                           ' 

117. 

fe)Jt/l> 

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S3 

^* 

t^^T- 

4B 

^ 

5 

~ 

XI              <5 

^ 

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-^  ^ 

=*&•  &— 

—  «*  -^  —  1 

^         1 

r- 

T     P 

i  —  (a  zi 

JZl~ 

\           1  ^~ 

JS-. 

1  —  iffi  —  1 

^'       1 

-£2- 

-£2. 

MpJ.S  

—  S  

^--^ 

5 

& 

--, 

The  Cantus  Firmus  is  in  the  Bass,  the  Counterpoint  in  the  Tenor. 


118. 

Cp. 

c.  f. 


:f= 


5^= 


^ 
=^ 


COUNTERPOINT  IN  THE  INNER  PARTS. 


45 


Or  with  a  modulation  in  the 


x^ 

ss 

M\           & 

^2 

E 

\S-ly 

1 

1 

tir 
J        ,, 

ZS 

-^1          |x 

& 

-<j      1 

J    , 

1 

/^\«it                             £*^ 

'^                 ^x 

•^X                       —  J 

15 

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f*t                                                                    C-^?_                j        y  ^x               .^ 
cs^^                    J             ^                                                                                       ^                                      L^r"            /^ 

/<(~\«4f                              1 



(£x*                *•* 

—  s;  

,2 

Exercises. 

NOTE. — The  cantus  finnus  is  to  be  transposed,  for  the  alto  or  bass,  into  some 
other  suitable  key. 


119-3t= 


12O.  - 


1  / 

\ 

-&— 

Of 

^ 

—    \ 

h._  ^l 

J 

121. 


§  14.  After  these  exercises  we  may  advance  to  others,  in  which 
the  counterpoint  will  be  set,  sometimes  alternately  and  sometimes 
simultaneously,  in  two  and  three  parts  against  the  cantus  firmus. 
The  simple  mechanical  process  would  be,  first  to  work  out  the  cantus 
firmus  in  equal  counterpoint,  and  then  to  write  the  contrapuntal 
movement  in  any  part  or  parts,  in  turn,  wherever  this  could  be  effected 
most  easily  and  naturally.  However,  we  by  no  means  recommend 
this  process  to  the  student.  For  it  is  not  desirable  that  he  should 


46 


UNEQUAL    COUNTERPOINT. 


work  a  contrapuntal  movement,  piecemeal,  into  an  exercise  previously 
worked  out  without  reference  to  a  freer  motion  of  the  parts.  An  un- 
skilled beginner,  to  be  sure,  may  be  allowed  to  employ  this  style  of 
work  for  his  first  attempts.  But  he  should  soon  learn  to  conceive  his 
work  in  a  freer  and  more  artistic  style,  in  which  the  contrapuntal 
movement  to  the  cantus  firmus  is,  from  the  very  start,  thought  out 
and  invented  to  fit  the  progression  of  the  latter.  Simultaneous  con- 
trapuntal movement  in  two  or  three  parts  may,  occasionally,  have  an 
excellent  effect.  But  too  long  continued  movement  in  several  parts 
together  has  a  tedious  effect.  By  way  of  illustration,  eight  workings- 
out  of  cantus  firmus  No.  120  are  given  below.  The  first  example  of 
each  pair  is  simpler,  only  one  part  having  the  movement  in  alternation 
with  another;  whereas  the  second  example  exhibits  a  more  varied 
movement  in  two  or  thiee  parts.  But  the  'student  is  not  required  to 
observe  this  order;  he  may  employ  the  contrapuntal  movement,  at 
pleasure,  in  one  or  two  parts,  or  sometimes  even  in  three,  in  one  and 
the  same  exercise. 


The  Cantus  Firmus  in  the  Soprano. 


122. 


or:    . 


—^ 

f2 

5_ 

dt±: 


COUNTERPOINT  IN  SEVERAL  PARTS. 


47 


123. 


^ 


//t\^ 

^y 

_ 

E~ 

—  .,     ^? 

^^ 

VM  J                         ',  "^                        /y 

^y          ' 

*_                     S3 

^y                 1 

«-/      >»—  ^1               1 

1 


1                   J^ 

^                             \ 

""^J           1 

£_ 

^ 

JH. 

SS*  fj                     j^ 

£j 

C^L"7  ^  1  

\  —  —  &  — 

The  Cantus  Firmus  in  the  Bass. 


124. 


r 


Ri — Tq 

— <S> -4—1 

— US' J 


» 


ar     a^= 


m 


r — rr 

P$= 


32 


125. 


J 


UNEQUAL   COUNTERPOINT. 


0  t?                 I 

-!  1- 

2J£$                 —  J— 

—  <5i  ^ 

<9            —  *-=— 

^  —  z?  

V               -<&- 

1                  ^  

1    *          ^ 

„ 

j    J-     A 

C^\*     hi              ^"^ 

• 

^F^_^ 

2 

ex 

ex 

^            1 

The  Cantus  Firmus  in  the  Tenor. 


126. 


X3  I         gX 


-tr.  2 

!                        _*. 

-       i               -| 

rf£k  ^^ 

& 

^^  —  ^  P  — 

?5  

&  &  

tr   -r  -f 

-x^,-                               e> 

/»"\«     K 

&  

127. 


Tf-u   /i     s 

»          & 

X5 

"{?           in   J 

f(T\      1C 

r  ^ 

i           r  -1 

^  K                                     ^ 

fi? 

^^ 

x>                        *~ 

--1            .V'j 

0          f      I 

1 

-&- 

1 

I^/»~lT7tJ"                  —  ^ 

—  ^  ~f5  — 

—  —  

^^•^fl      VI  i'        r*"J 

r          xs. 

^,            1 

T~, 


^'  ^3- 


g;- 


-^ 


COUNTERPOINT  IN  SEVERAL  PARTS. 
The  Cantus  Firmus  in  the  Alto,  transposed  into  Eb. 


49 


128. 


Sv^ftM  —  -$~ 

S  E 

—  ^  

-1 

fin         &  ^- 

^/ 

1551                T 

,  j 

J   j 

fm\'   hi     i            & 

0                 1 

HZsptlJl        & 

_ 

X3               -,    . 

^wb  CIC 

---j 

/^» 

_    f  n 

fl  h  ^J        1'  —  -  '        '                      ' 

^^          . 

/K-p-b  35  —  — 

^      & 

"•  \        \ 

—  ~s^&  ^  — 

—  /5  

^  — 

-«>- 

_                            1                               ~er                -zr 

C^\*   K 

^N?  —  —  

—  s»  — 

—  &  

129. 


0  \) 

r—  ^  h-i 

1  1  7^  1 

/jf  b^/l*  1  —       •  ^ 

=  r~ 

—  i  1  — 

—  H  j— 

I?K\        P^l*'                              y*' 

"</      i 

2 

5;        *^ 

^-    ^  -* 

51         A' 

2  ^,     51 

1*3 

1                              t^  t-^                                ^                                    <-—  '   ^-- 

J      J      J       J        !       «>       «                 « 

/•^i«  u  i    szri 

c^ 

J 

[^•i  7  /  »            & 

-_ 

a 

EZ5J3E 

--j 

^ 

1 

J:    J 


The  following  exercises  are  to  be  worked  out  in  the  manner  shown 
in  Examples  No.  122  to  129.  When  the  cantus  firmus  is  in  the  bass 
or  alto,  it  may  be  transposed  into  other  keys,  wherever  the  range  of 
the  voices  may  require  such  transposition. 

Exercises. 


50 


UNEQUAL   COUNTERPOINT. 


131. 


132. 


Should  other  exercises  be  needed,  any  suitable  cantus  firmus  in 
former  exercises  may  be  selected  for  working  out  in  this  manner. 


CHAPTER    IV. 

Counterpoint  of  Four  Notes  against  One  in  the 
Cantus  Firmus. 

§  15.  In  a  contrapuntal  movement  of  four  notes  against  one  in  the 
"cantus  firmus  (i.  e.,  4  quarter-notes  against  1  whole  note),  the  follow- 
ing rules  govern  the  progression  of  all  the  parts  : 

1.  The  first  note  in  each  measure  must  be  a  chord-note. 

2.  Between   two  chord-notes,   passing-notes   in    stepwise  pro- 

gression may  be  introduced. 

Avoid  changing-notes,  because,  at  the  beginning  of  a  measure, 
they  often  conflict  with  the  first  rule,  and,  in  the  middle  of  the 
measure,  with  the  second.  We  do  not  mean,  however,  that  changing- 
notes  ought  invariably  to  be  excluded  from  all  contrapuntal  work. 
In  the  more  complicated  problems  of  Canon  and  Fugue,  their  intro- 
duction is  justifiable,  and  may,  indeed,  be  of  the  finest  effect.  But, 
in  general,  it  is  well  to  avoid  their  use  as  far  as  possible  in  all  con- 
trapuntal work,  even  in  the  canon  and  fugue ;  for  the  changing-note, 
whether  entering  from  above  or  below,  always  bears  the  character  of 
an  unprepared  suspension,  and  is,  therefore,  not  wholly  in  keeping 
with  the  strict  style.  (See  Manual  of  Harmony,  §57.) 

A  contrapuntal  movement  of  four  notes  admits  of  no  harmonic 
connection,  and  but  few  and  occasional  suspensions.  A  suspension 
must  always  be  prepared  by  a  leap  ;  consequently,  the  following  pre- 
parations are  not  satisfactory. 


QUARTER-NOTES  IN  SOPRANO, 
a.  b. 


51 


133. 


a^£ 


_] — J — JrrpJ_J__| — U=^l      |     -!      \^ 

^=|==  -^=^[-^— j_jII3^ 


A        i         .        J         k  —  ^  !                          i 

I/  1  —  1         |        *        ^ 

•            «            _i             i 

*            * 

(3)"     *        * 

S3                             1 

S2 

/^                             1 

* 

6»v       ^ 

CZa 

^b 

All  such  preparations  of  suspensions  are  bad.  The  worst  is  that 
under  d,  for  in  this  case  the  after-striking  seventh  (and  a  major 
seventh,  besides),  coming  from  the  octave,  is  retarded  in  its  resolution 
and  has  to  serve  as  a  preparation  for  the  suspension. 

Even  suspensions  prepared  by  a  leap,  e.  g., 


134. 


ought  to  be  seldom  employed.  Both  notes  of  the  leap  must,  of  course, 
be  chord-notes.  Suspensions  have  the  best  effect  at  the  close.  Sev- 
eral, or  many,  suspensions  interrupt  and  disturb  the  running  move- 
ment in  quarter-notes.  Contrapuntal  progressions  of  this  kind  belong 
rather  to  the  modern  free  style,  so  to  speak,  than  to  the  strict  style. 
E.g., 


i 

4 

» 

1 

LM)    '"' 

sy 

^-,       i 

Ir- 

-x?-                                                      ^i2. 

/ST*     i 

^2 

i^^}  •  /|t 

/-^, 

W1O    \j  ,- 

135. 


XL  f  1*                      1     * 

*     m 

m 

*  *    • 

i 

fmlp      J      *      m 

—  . 

<Z—\ 

^ 

/i^i 

•^ 

^y 

-5>-                            ^2_                                                               £2                            iS>- 

>^A«      . 

/«^ 

EZiZlI 

.-.n  -  •- 

Q. 

.1 

52 


UNEQUAL    COUNTERPOINT. 


The  very  necessity  of  preparing  the  suspension  by  a  leap,  spoils 
the  diatonically  melodic  leading  of  the  part.  The  melodic  progression 
of  good  counterpoint  is  always  predominantly  stepwise.  For  this 
reason  we  must  forbid,  in  the  counterpoint  in  quarter-notes,  all  chord- 
figures  which  do  not  contain  at  least  one  diatonic  step  (the  after- 
striking  seventh,  or  the  ninth  progressing  downward  from  the  tenth). 
This  diatonic  step  must  be  formed,  moreover,  by  the  two  last  quarter- 
notes  of  the  measure. 


Bad. 


Good. 


Fairly  good. 


136. 


m 


In  this  case  the  after-striking  seventh  progressing  downwards 
from  the  octave  is  the  most  suitable  note ;  a  ninth  following  a  tenth 
would  be  less  so.  In  certain  cases,  three  successive  chord-notes  may 
be  followed  by  a  diatonic  step  upward,  e.  g., 


but  a  chromatic  step  after  three  such  chord-notes  could  be  sanctioned 
only  in  rare  cases,  e.  g. , 


nnm 


Bad. 


Good. 


Good. 


g^    m 


Broken  triads,  like  those  below,  are  not  allowable. 


137. 


1 — •— 


FOUR  QUARTER-NOTES  IN  SOPRANO. 


53 


A  mere  embellishment  of  one  whole  note  by  the  four  quarter- 
notes,  throughout  several  measures,  must  be  carefully  avoided. 


138. 


n                         1        1                     iii 

i 

!                 !              -' 

f\.           /i^               \f**T         ^                                                                         ^ 

7^\     m            ^ 

J 

I?1\      VI  J                              ^> 

\  j^J     ^_ 

yVl  J                                       -^ 

^*^ 

~&~                                                                              & 

^} 

5h^Z    \1/                          (^ 

The  soprano  part  in  Ex.  138  illustrates  this  sort  of  progression, 
which  is  extremely  awkward.  One  is  sometimes  obliged  to  employ 
such  embellishments  of  a  whole  note  ;  but  then  the  following  figures 
should  be  used  in  alternation,  as  may  appear  most  suitable. 


139. 


By  the  alternation  of  such   figures,  the  following  whole  notes 
might,  as  an  extreme  illustration,  be  embellished. 


14O. 


t^-Ttr »- 

EilEEE 


54 


UNEQUAL    COUNTERPOINT. 




-iS>  

•75  

=5  

-<3>—  

«7 

n    u              PI 

i 

i 
f  •  ^ 

1 

f-  

EE 



. 

i  1= 

i  ^  0  — 

—~  1 

But  we  again  warn  the  student  emphatically  against  employing 
the  purely  mechanical  process  of  first  working  out  the  exercises  in 
equal  counterpoint,  and  then  writing  out  in  quarter-notes  the  whole 
notes  of  the  part  in  which  the  contrapuntal  movement  is  to  be.  Such 
counterpoints  usually  exhibit  very  plainly  their  forced  process  of  cre- 
ation. For  those  melodic  and  harmonic  progressions,  which  are  the 
best  and  most  natural  in  equal  counterpoint,  are  frequently  not  so 
well  adapted  for  the  working-out  in  unequal  counterpoint. 

In  the  minor  mode  the  melodic  scale  is  used  almost  exclusively 
for  the  diatonic  counterpoint  in  quarter-notes.  The  augmented  sec- 
ond of  the  harmonic  scale  must  never  be  written  in  ascending  pro- 
gression. In  descending  progression  it  may  be  occasionally  employed 
in  advanced  counterpoint  (canon  and  fugue).  But,  for  our  present 
work  in  single  counterpoint,  its  use,  even  descending,  should  be  wholly 
avoided.  For  progressions  in  the  melodic  minor  scale  great  care 
should  be  taken  not  to  write,  in  the  counterpoint,  a  chromatic  altera- 
tion of  any  tone  sustained  in  some  other  part ;  or  vice  versa.  But 
even  when  no  other  part  sustains  the  natural  tone  while  the  counter- 
point takes  a  chromatically  altered  tone,  or  vice  versa,  all  tones  not 
belonging  to  the  harmony  must  be  avoided.  Consequently,  the  fol- 
lowing progressions  are  out  of  the  question  : 

Out  of  the  question. 


141.  \ 


c.  f. 


f\ 

,      1 

1     J             1 

|        , 

\)            .^ 

i     *     • 

1              1 

•XT     /J4          \* 

J 

*            •     9 

J      J 

I/T\  \l  j          »s 

•    hm    M_I 

^VK                                                       tip 

1W  8* 

^           D*    fl^      1 

etc. 

/iV  1         " 

Z 

'^ 

^^y                                 1 

^v^^  

^  1 

-&  

1 

IV 


In  the  second  measure,  F%  is  wrong,  because  the  third  of  the 
triad  on  the  4th  degree  is  J7;  in  the  fourth  measure,  the  soprano  must 
not  take  G  while  the  tenor  has  G  #.  In  such  cases,  the  leading  of 
the  counterpoint  must  be  changed  ;  e.  g., 


142. 


c.  f. 


THE   COUNTERPOINT  IN  QUARTER-NOTES.  55 

1_ 


l-\ 


.^_,<     J 
•'  H 


We  now  add  a  few  illustrations  of  the  working-out  of  a  cantus 
firmus  in  minor.  The  several  parts  take  the  cantus  firmus  and  the 
counterpoint  in  alternation. 

The  Cantus  Firmus  is  in  the  Bass,  the  Counterpoint  in  the  Soprano. 

Cp. 


143. 


c.  f. 


—       1 — -i — I —  j — i 

~*    0    j*J    *   I"  !    ^J     ^~l~ 

Z±3*=5t=  =I 


n 

.  i  |             J     J      |      1    .     -|       I              | 

Jr  * 

m     "                                   *    \    m              m      * 

KB-   8*   :+=S3   « 

\                              \    " 

a 

1  —  &  —                   '     ^                           & 

-G>- 

/>y 

^-\^                        ^^ 

f^\* 

L^y*              f  1 

1     t^/ 

i^  r>*               ^ 

a                        n  ....  .  ...         1 

The  Cantus  Firmus  is  in  the  Soprano,  the  Counterpoint  in  the  Bass. 


c.  f. 


144. 


Cp. 


^=^=tSEf^="EEt=r=rEF 

EF-r=F=Fg^=:= — h^-MHzz 


56  UNEQUAL   COUNTERPOINT. 

The  Cantus  Firmus  is  in  the  Alto,  the  Counterpoint  in  the  Tenor. 


C.f. 

145.  I 

Cp. 


zjr7)-jZJ[4j_iLJ 


^ 


ff\\  72  

^ 

1 

w-  —  ^  

_  

-^  —  1 

|     1                 |    j    J     J.J:J.J."    J          J     J 

9       ^r 

/s-     i 

[^/«ff         *                          ™ 

m 

-4tx^    

a. 

The  Cantus  Firmus  is  in  the  Tenor,  the  Counterpoint  in  the  Alto. 


Cp. 

146. 

C.f. 


K—-&'9- 


-&- 


Exercises. 


147. 


148. 


<g_. 


Q  UAR  TER-NO  TES 

/TV  SEVERAL   PARTS. 

57 

i 

l>  -^  */!* 

Z5 

&  

^ 

£s 

L^^-x  *•  1  J      ^^ 

-^ 

£•*• 

<S>           1 

[^             ' 

^"^ 

_           1 

i£y*/U 

~& 

_<fi  



QQIB 

_-Q^_ 

«C 

150. 


The  cantus  firmus  may  be  transposed  when  the  range  of  the  part 
having  it  renders  this  necessary. 

§16.  After  writing  the  above  exercises,  paying  attention  chiefly 
to  the  leading  of  the  part  having  the  counterpoint  in  four  quarter- 
notes,  the  student  may  proceed  to  the  exercises  given  below,  which 
occur  more  frequently  in  practical  work.  In  them,  the  counterpoint 
is  to  pass  from  one  part  to  another,  in  alternation,  of  the  three  parts 
in  which  it  may  be  written  ;  or  two,  or  even  all  three  parts,  may  carry 
out  the  movement  simultaneously,  though  this  must  not  occur  too 
often  or  too  continuously,  as  it  would  make  the  contrapuntal  move- 
ment too  heavy  and  complicated.  Just  now  no  new  rules  will  be 
needed  for  these  exercises ;  we  shall  remind  the  student  of  only  one 
(see  Manual  of  Harmony,  §56,  Ex.  291),  namely,  that  where  the 
counterpoint  has  four  notes  against  one  in  the  cantus  firmus,  either 
the  major  or  the  minor  ninth  may  enter  unprepared,  by  a  leap,  in 
case  it  is  supported  and  strengthened  by  the  seventh.  This  is  illus- 
trated in  Ex.  151. 


151. 


c.f. 


1         *                         * 

^^ 

m      *  '      *      m 

X  k    / 

J 

1     '    « 

1 

ffh   *• 

j       ^^ 

if 

~         1 

\ 

•  i    ' 

2 

***^_ 

-^ 

^          1 

^^ 

ij 

j^jj 

J 

1             1 

_J_  _J_ 

1    i 

I     _ 

/^A«     ^ 

9 

, 

.     J     I 

[R/-,    I// 

V       ^ 

*^^ 

0    J 

^^a    V 

y 

XT3 

o"~^     !    I    I 

.  i  *  j 

rtJ     ^  J 

^  Jj 

Jf  L-7  0  —  !  —  •'  —  f  — 

-H  •  ^  

^»r~^=*= 

/*  — 

f^|^\  L' 

m      & 

/^ 

°    \ 

\isJJ                 jpS> 

i 

^J     1 
rr«~s  —  *  —  r 

j_       _     |   .. 

1        I                1 

,  j  j  j-, 

j_  i  j 

*  ^  — 

1 

^  —  ^-^  E 

—  ^g  - 

^    1 

The  unprepared  ninths  entering  by  a  leap,  and  supported  by  a 
seventh,  are  marked  *. 


58 


UNEQUAL    COUNTERPOINT. 


To  show  how  the  following  exercises  are  to  be  worked  out,  exam- 
ples are  added  with  a  cantus  firmus  accompanied  by  a  contrapuntal 
movement  in  four  quarter-notes,  in  which  the  three  other  parts  par- 
ticipate. 


The  Cantus  Firmus  is  in  the  Soprano. 


c.  f. 


152. 


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m     £ 

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KB. 


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1-rfT 


N.  B. — The  resolution  of  a  suspension  may  be  retarded  by  intermediate  notes. 
(See  Manual  of  Harmony,  §56,  Ex.  289.) 


The  Cantus  Firmus  is  in  the  Bass. 


153. 


c.  f. 


:^t 


z^^i^yziq 


E?$: 


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QUARTER-NOTES  IN  SEVERAL  PARTS. 
The  Cantus  Firmus  is  in  the  Alto. 


59 


7LIP 

*    0 

a           * 

9        ^ 

C.  f. 

tn\  \iy 

JJ 

f^ 

t)        -&-                 " 

154. 

-J-.          J_                                        1       J     I 

<wv  i 

& 

•^                   »         » 

V^J'f  r                      m     m 

A 

SSS&     ra          f.. 

_l  *  — 

S3 

—  •*• 


The  Cantus  Firmus  is  in  the  Tenor. 


155. 

c.  f. 


1  I 1 — « 1 • m I      *£»' I — -*^ 


r^T 


**U 


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1 — ^ — 


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^> 

— 

Imitative  figures,  like  those  in  the  last  measures  of  Ex.  1555  lend 
a  peculiar  charm  to  the  contrapuntal  parts. 


60 


UNEQUAL    COUNTERPOINT. 

Exercises. 


-^^—& — vLsi — 


157. 


=^ tgxo— 


RP 


ISS.RSi 


159. 


REMARK  ON  THESE  EXERCISES. 

Brief  modulatory  transitions  into  related  keys  may  be  occasionally 
permitted.  Now  and  then,  too,  a  chromatic  passing-note  (an  altered 
fifth  is  the  best)  may  be  employed  ;  e.  g., 


16O. 


c.  f. 


f/|\  1     y           9&        *' 

S2 

\M-/ 

tr 

\       1 
J       1       1       J 

J    J    ^  *L 

/^'\«    i 

TLjP 

l^y  *V  4 

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tj 

V  J  J  J-  J  v  j  j  „ 

jSi. 

f^\m 

'^"^" 

&     * 

—  _  «i  

I 


However,  a  series  of  chromatic  notes  is  to  be  avoided.     (See  Man. 
of  Harm.,  §57,  Ex.  301  and  302.) 


THREE-PART  EQUAL    COUNTERPOINT. 


61 


CHAPTER    V. 
Three-part  Counterpoint. 

§17.  Three-part  equal  counterpoint  must  be  so  written,  that  the 
harmony  may  at  all  times  be  readily  recognized  ;  although  we  have 
only  three  parts  for  the  presentation  of  four-part  chords.  It  is  quite 
easy  to  follow  this  rule,  because  the  inner  part  (alto  or  tenor)  has 
more  room  to  develop  an  independent  leading.  For  this  reason  the 
inner  part  will  be  able  to  take  leaps,  particularly  of  a  fourth  or  fifth, 
oftener  than  in  four-part  writing ;  and  this  will  be  advisable  when 
such  leadings  result  in  making  the  harmony  fuller.  The  interval 
between  alto  and  soprano  may  be  as  wide  as  a  tenth,  or  even,  occa- 
sionally, an  eleventh.  Beginning  and  close  have  the  best  effect  with 
all  three  parts  in  unison.  The  chord  of  the  sixth  of  the  triad  on  the 
7th  degree  may  sometimes  be  used  instead  of  the  dominant  chord. 
Similar  or  parallel  motion  in  all  three  parts  should  be  sedulously 
avoided ;  but,  as  an  exception,  the  chord  of  the  sixth  of  the  triad  on 
the  7th  degree  may  follow,  in  parallel  downward  progression,  the 
chord  of  the  sixth  of  the  triad  on  the  1st  degree  ;  e.g., 


The  reverse  progression,  upward,  is  less  desirable  ; 


•  but  even  this  may  occasionally  occur.  Progressions  like  the  next- 
following  must,  however,  never  be  written,  for  they  are  repugnant  to 
the  nature  of  contrapuntal  writing. 


161. 


The  seventh-chord  may  sometimes  be  employed  without  a  third. 
(See  Manual  of  Harmony,  §36,  Note.)     Covered  octaves  cannot  be 


62 


THREE-PART  EQUAL    COUNTERPOINT. 


avoided  at  the  close  when  the  latter  is  formed  by  the  unison.  For  the 
rest,  the  student  should  bear  in  mind,  that  all  species  of  covered 
fifths  and  octaves  have  a  harsher  effect  in  three-part  writing  than  with 
four  parts,  and  that  the  leading  of  the  parts  requires  greater  caution 
on  this  account.  The  next  three  examples  illustrate  the  working-out 
of  a  cantus  firmus  in  three-part  equal  counterpoint. 

The  Cantus  Firmus  is  in  the  Soprano, 
c.  f. 


162. 


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—  *&  

IV 

—  ^  

2 

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^-S  

The  Cantus  Firmus  is  in  the  Bass. 


163. 


c.  f. 


D  ** 

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In  the  measure  before  the  last  the  sustaining  of  the  bass  note,  in 
the  cantus  firmus,  is  covered  by  the  decided  movement  of  the  highest 
parts. 


UNEQUAL    THREE-PART  COUNTERPOINT. 
The  Cantus  Finnus  is  in  the  Alto. 


63 


c.  f. 
164. 


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ry 

irn  -*E 

2 

ssz 

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f2 

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a: 

V^^^     TL 

Should  we  propose  to  write,  to  this  cantus  firmus,  a  counterpoint 
in  half-notes  in  either  of  the  other  parts,  or  partly  alternating  between, 
and  partly  together  in,  the  latter,  we  should  be  guided  by  the  rules 
already  given  for  four-part  writing.  However,  in  three-part  writing, 
even  with  the  contrapuntal  movement  in  half -notes,  an  occasional 
chromatic  passing-note  may  be  more  readily  permitted,  where  it  lends 
greater  richness  and  fullness  to  the  harmony  than  could  be  obtained 
with  another  leading  of  the  part.  Thus,  the  G  $  on  the  second  beat 
of  measure  5  in  Ex.  165,  and  the  A  $  in  measure  3,  Ex.  167,  are  not 
incorrect.  We  lead  the  bass  intentionally  in  this  manner,  so  as  to 
show  the  student  that  he  may  occasionally  employ  such  progressions, 
though  not  too  frequently  or  in  too  rapid  succession.  We  hardly  need 
to  observe,  that  in  either  case  the  chromatic  note  might  easily  have 
been  avoided,  in  the  manner  shown  at  the  close  of  the  examples  in 
question. 


The  Cantus  Firmus  is  in  the  Soprano. 


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KB. 

— ffl — — i— ^S? 


.X^  _^-ej 


NOTE. — At  N.  B.  the  true  tone  of  resolution  for  the  suspension,  the  note  D,  is 
omitted,  to  render  the  harmony  fuller.     (See  Manual  of  Harmony,  §56.) 


C.f. 
Cp. 

167. 

Cp. 


COUNTERPOINT  IN  FOUR  NOTES. 


65 


y    I      &*'  I      S>  _  ^     I — ^S?  I   gs,  "I 

^  -i — H=h— p^FF=h- = 

'       r-H — • '     '    ' ' 


Or: 


Work  out  the  exercises  in  the  same  way,  when  the  cantus  firmus 
is  in  the  alto  or  bass.  The  student  may  try  this  first  with  this  same 
cantus  firmus,  and  then  with  each  cantus  firmus  given  in  the  Exercises 
on  page  74. 


§18.  The  contrapuntal  movement  of  four  notes,  against  one  in 
cantus  firmus,  is  likewise  to  be  written  according  to  the  familiar  rules 
governing  four-part  writing.  Three  examples  illustrative  of  this 
point  are  given  below ;  the  cantus  firmus  is  in  the  alto. 


/5      ;-/  »             •     « 

1       '       ! 

,                 i 

fm      vp                   *     • 

1       i      *      • 

_ 

B2      2 

_t  -,    i   *  3 

168.  ( 

^^ 

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=  \ 

66  UNEQUAL    THREE-PART  COUNTERPOINT. 

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N.B. — Earlier  composers  always  wrote  a  whole  tone  in  such  cases;  the  semitone 
is  modern. 


C.  f. 

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COUNTERPOINT  IN  FOUR  NOTES. 


67 


i  _    I         i 


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« 

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; 

The  work  is  to  be  carried  out  in  the  same  manner  when  the  cantus 
finnus  is  in  the  soprano  or  bass.  Each  cantus  firmus  in  the  following 
exercises  is  to  be  set  in  all  parts  alternately,  and  worked  out  in  equal 
and  unequal  counterpoint,  as  shown  in  Exs.  161-169,  and  in  accord- 
ance with  the  preceding  suggestions. 


171 


Exercises. 
-s> — 


_ifi 


172. 


173 


m 


174. 


175. 


68 


TIVO-PA  R  T  CO  UNTERPOINT. 


CHAPTER    VI. 
Two-part  Counterpoint. 

§  19.  When  we  write  an  exercise  in  two-part  equal  counterpoint, 
we  must  begin  either  with  the  unison  or  with  the  octave,  or,  occa- 
sionally, with  the  perfect  fifth ;  and  close  either  in  unison  or  in 
octaves.  In  the  midst  of  the  exercise  no  perfect  interval  should  occur. 
Consequently,  unisons,  octaves,  and  perfect  fourths  and  fifths,  are 
not  to  be  employed.  The  only  permissible  intervals  are  the  imperfect 
consonances  (major  and  minor  thirds  and  sixths),  and  the  dissonances 
of  the  augmented  fourth  and  diminished  fifth.  These  intervals  are 
the  ones  best  adapted  to  render  the  harmony  easily  recognizable  and 
perceptible.  The  minor  seventh  and  major  second  are  not  suitable 
for  two-part  [equal]  counterpoint.  Successive  thirds  or  sixths  through 
more  than  two,  or,  at  most,  three  measures,  are  to  be  avoided  as 
repugnant  to  the  idea  of  counterpoint.  It  is  best  not  to  let  the  inter- 
val between  the  two  parts  exceed  a  tenth,  though  in  unequal  counter- 
point the  interval  may  occasionally  be  extended  to  a  twelfth.  But 
^the  two  parts  should  be  only  transiently,  so  far  apart,  for  otherwise 
they  cannot  support  each  other  so  effectively.  All  covered  fifths  and 
octaves  must  be  carefully  avoided  ;  even  the  covered  octaves  over  the 
semitonic  steps  are  forbidden.  (See  Manual"  of  Harmony,  §59.) 
Therefore,  do  not  write  : 


the  close  can,  consequently,  be  formed  only  by  contrary  motion  ;  e.  g., 


\ 


-Z5-^^-^ 

First  we  give  an  example  in  equal  counterpoint.     The  cantus  firmus 
is  in  the  alto. 


-<9 ^ \—&—\ 

— -%~          ~ 

a 1 — fs- — I — 


UNEQUAL    TWO-PART  COUNTERPOINT. 


69 


For  unequal  counterpoint  in  half -notes  we  give   the  following 
rules : 

1.  The  suspension  of  the  Fourth  before  the  Third,  the  Fifth 

before  the  augmented  Fourth,  and  the  Seventh  before  the 
Sixth,  are  allowable. 

2.  The  perfect  or  diminished  fifth  may  follow,  on  the  second 

beat  and  in  stepwise  progression,  after  a  sixth.  Such  an 
"  after- striking  "  fifth  then  bears  the  character  of  a  pass- 
ing seventh,  and  must  be  led  downward  by  a  step ;  e.  g., 


177. 


A        &       ^ 

fm             ^ 

(2 

^ 

3.  An  after-striking  fourth,  entering  by  a  leap,  is  to  be  avoided. 

Bad.  Bad. 

r-0—  -.- 

178. 


On  the  other  hand,  a  passing  fourth,  progressing  downward  by 
a  step,  is  permissible,  because  it  bears  the  character  of  a 
passing  seventh,  and  resolves  downward  ;  e.  g., 


4.  An  after-striking  octave  or  fifth  is  allowable. 


Good. 


Good. 


Good. 


ISO. 


5.  Two  successive  major  thirds  are  forbidden. 

6.  A  passing  seventh  is  also  permitted  at  the  beginning  of  an 


An  illustration  follows  ;  it  exhibits  a  counterpoint  in  the  soprano, 
and  another  in  the  tenor,  written  to  the  same  cantus  firmus. 


) 

ft2. 

TWO-  PART  COUNTERPOINT. 

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When  a  counterpoint  of  four  notes  against  one  in  the  cantus 
firmus  is  written,  one  may  also  sometimes  begin  with  a  third  or  a 
fifth;  e.  g., 


183. 


^q= 


Finally,  all  the  rules  already  given  are  valid.     No.  184  is  an 
example  of  this  species  of  counterpoint. 

184. 


Cp. 


C.  f. 


Cp. 


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— \ • h — F- 


fe 


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UNEQUAL    TWO-PART  COUNTERPOINT. 


71 


*    r    •  i 

I       1       I 

1 

i      -L    i-    k    1 

•    r 

JJ4 

j 

.r   • 

i,    iJ 

j_ 

<5>                       1  _ 

«           i       i 

[[•t  jt  ^ 

! 

r-*^ 

[jS 

. 

— §—»= 


To  this  we  add  the  following  observation.  A  contrapuntal  move- 
ment of  any  considerable  length,  for  two  vocal  parts,  is  something 
which  is  probably  never  written  in  our  time,  so  accustomed  to  the 
employment  of  fuller  and  richer  harmonies.  Per  contra,  a  short  two- 
part  episode  in  a  polyphonic  vocal  movement — for  instance,  in  a  vocal 
fugue — may  often  have  a  good  effect.  It  then  serves  as  a  contrast  to 
the  richer  polyphonic  development  preceding,  and  affords  the  ear  a 
point  of  repose,  as  it  were.  Different  conditions  obtain  in  a  two-part 
instrumental  movement,  in  which  the  harmony  can  be  suggested  by 
more  florid  figuration,  and  will  thus  appear  fuller.  This  may  be  seen, 
for  instance,  in  two-part  fugues  ;  we  refer  the  student  to  J.  S.  Bach's 
-£7-minor  fugue,  No.  10  in  Vol.  I  of  the  Well-tempered  Clavichord. 


Exercises. 


186. 


187. 


^^ 

PART  THE   SECOND. 

DOUBLE    COUNTERPOINT. 


CHAPTEK    VII. 

§20.  The  term  Double  Counterpoint  is  applied  to  a  contrapuntal 
part  written  in  such  a  manner  as  to  be  invertible,  in  relation  to  the 
part  to  which  it  is  set,  by  an  octave,  or  a  tenth,  or  a  twelfth.  We 
teach  only  three  species  of  double  counterpoint,  namely,  in  the  octave, 
in  the  tenth,  and  in  the  twelfth.  Earlier  text-books  also  contain  rules 
for  double  counterpoint  in  the  ninth,  eleventh,  thirteenth,  and  four- 
4eenth.  Contrapuntal  parts  invertible  into  all  sorts  of  different  in- 
tervals can,  however,  be  used  only  under  very  stringent  limitations, 
so  that  they  seldom,  or  never,  are  employed  in  practical  composition. 

We  commence  with  double  counterpoint  in  the  octave,  in  a  two- 
part  movement.  We  need  add  nothing  here  to  the  now  familiar 
rules  for  two-part  single  counterpoint,  except  that  the  interval  between 
the  parts  must  now  not  exceed  an  octave,  for  otherwise  the  inversion 
of  the  parts  would  be  rendered  illusive,  while  the  inversion  by  a 
double  octave  would  spread  the  parts  too  far.  Ex.  188  is  an  illustra- 
tion in  which  the  contrapuntal  part  may  be  set  either  as  a  soprano  or 
as  a  tenor  to  the  cantus  firmus  in  the  alto.  From  here  onward,  the 
cantus  firmus  will  no  longer  be  given  only  in  equal  notes,  like  those 
hitherto  given  for  the  exercises  in  single  counterpoint ;  this  will  make 
the  cantus  firmus  less  rigid.  In  writing  the  counterpoint,  special  care 
must  be  taken  to  make  it  contrast  rhythmically,  as  far  as  possible, 
with  the  cantus  firmus. 

With  a  cantus  firmus  of  this  kind,  to  which  a  rapidly  moving 
counterpoint  is  set,  a  tie  between  two  quarter-notes,  connecting  two 
harmonies,  is  permitted.  Besides,  a  quarter-note  entering  by  a  step 
may  be  utilized  to  prepare  a  suspension.  The  case  is  now  a  different 
one,  for  the  reason  that  as  a  general  thing  not  four,  but  two  notes 
(quarter- notes)  are  set  against  one  half -note  in  the  cantus  firmus. 


TWO-PART  DOUBLE   COUNTERPOINT. 


73 


188 


c.f. 


Inversion. 


-&• (2— I— *± *- 


—5*- 


It  will  be  seen,  that  only  such  intervals  and  progressions  are  pos- 
sible as  were  allowed  in  two-part  single  counterpoint.  Intervals  like 
the  augmented  sixth,  for  instance,  can  not  be  used  in  the  latter,  and 
must  also  be  excluded  from  the  present  exercises.  Under  No.  189  we 
furnish  an  illustration  of  this  species  of  counterpoint.  From  this  the 
student  will  perceive,  that  transient  modulations,  which  do  not  lead 
too  far  away  from  the  principal  key,  are  permitted. 


Inversion. 


?rT7    ¥-   T&r 


-1 4 


T   ^-  U     '  f '  ^ 


Or: 


DOUBLE   COUNTERPOINT. 

Exercises. 


19O. 


To  this  cantus  firmus  a  lower  part  is  to  be  written  ;  for  the  inver- 
sion, the  cantus  firmus  is  to  be  transposed  into  the  octave  below,  the 
counterpoint  remaining  where  it  is. 


191. 


Si 


To  this  alto,  a  soprano  is  to  be  written  as  a  counterpoint,  and  then 
to  be  inverted  into  the  lower  octave,  the  cantus  firmus  remaining 
where  it  is  ;  work  out  192  and  193  in  the  same  manner. 


=*= 


192. 


193. 


Double  Counterpoint  in  the  Octave,   in  Three-part 

Writing. 

§21.  When,  to  a  cantus  firmus  in  the  bass,  we  set  a  soprano  and 
alto  in  such  a  manner  that  the  soprano,  transposed  an  octave  lower, 
will  serve  as  a  tenor  to  the  bass  and  the  alto,  the  following  conditions 
must  be  observed : 

1.  Soprano  and  alto  must  not  lie  further  apart  than  an  octave. 

2.  They  must  not  form  such  parallel  fourths  as  would  result, 

when  they  are  inverted,  in  forbidden  parallel  fifths ;  e.  g., 

Inversion. 


Inversion. 


194. 


W^  =3 — 

r— »-g — j— H — HE* — * — I 


On  the  other  hand,  parallel  fourths  of  this  description, 


v 


are  permissible  where  the  bass  progresses  in  contrary  motion  ;  e.g., 


THREE-PART  DOUBLE   COUNTERPOINT. 

Inversion. 


75 


195. 


=4 aU 


=*— l-g— q=^^ 

— ,g =J=g  ^        I— ^ 1 


3.  The  soprano  must  not  approach  the  bass  nearer  than  an 
octave,  otherwise  it  will  cross  and  progress  below  the  bass 
on  inversion. 


Not  so : 


Inversion. 


196. 


-&- 


-27- 
-<S>- 


4.  The  actual  suspension  of  9  before  8  between  soprano  and 
bass  must  also  be  avoided,  because  inversion  gives  a  sus- 
pension of  2  before  1. 


Not  so : 


Inversion. 


ffh"  ^^^ 

g  —  a  —  -n  — 

-\ 

V<j-/ 

*            <v        1       1 

\ 

1                                           7*~          ??""  "^^  ^ 
1    N  ^i 
98                                        21 

fiESs 

1^ 

[^x*                 ^^ 

f? 

^^  '  

=£— 

197. 


But  where  the  soprano  is  two  octaves  above  the  bass,  instead  of 
one,  such  a  suspension  may  be  written  ;  for  in  this  case  it  will  result, 
on  inversion,  in  a  suspension  of  9  before  8. 

x*"     ~ — .  II  I  I         Inversion. 


198. 


XL     /|» 

—  ^  —       \—&  — 

3     & 

lv|)   vi/  —  &  — 

—  °-  H  

—  —  |  &<9  

—  &            S3  

&               !*2                • 

9 

i 

9           8 

^  . 

A       [^ 

9          8 

•n 

fjftV      i 

"^ 

«     -*"     i 

[CJ.  /U     ^ 

c 

s^'  m 

t  ' 

-  L 

76 


DOUBLE   COUNTERPOINT. 


Attention  must  be  paid  to  the  leading  of  the  alto,  inasmuch  as 
the  latter,  on  inversion  of  the  soprano  into  the  octave  below,  becomes 
the  highest  part.  An  illustration  of  this  species  of  counterpoint  fol- 
lows. 

4 


Cp.      / 

199. 

C.  f.     I 

/r    5  /|*                2. 

1  ^ 

^_ 

^^                                                                             A 

-| 

r 

/w~\*4+      - 

— 

}i 

Pv/V  i\*        ty 

& 

-t  *  i 

—  *  — 

^"^     if-*H  

—  I  

—  *  —  i 

fir*^—  '—  i  —  P 

—  ^  

1  

*       m 

J    ^           -r  r  r  T 

-G>-                                          ^^ 

i   i 

fjB^tt 

P^*IC 

'w7  I    «  ,    . 

«y 

Inversion. 


/L    »  I  * 

I(T\    —\t 

-^ 

2 

H2 

2_ 

•         « 

»J                   ^ 

^ 

Pn 

^         ^^ 

~"^   i             1           i 
^ 

-*-        4 

f^~ 

/w^«tt      i 

% 

[^•iffji      /»                ^ 

s-j 

m          m 

S2  s  M^ 

f          » 

"* — - — * 


rp,LJ__J_i^ 

23^ ?__      g 


I         I 


It  amounts  to  the  same  thing,  of  course,  when  a  tenor  and  alto 
are  first  written  to  the  cantus  firmus  in  the  bass,  and  the  tenor  then 
inverted  to  the  octave  above  to  form  a  soprano  part.  But  in  this  case 
the  same  attention  must  be  paid  to  the  leading  of  the  tenor,  with  re- 
gard to  its  melodious  progression,  as  was  paid  to  the  alto  in  the  first 
exercises  of  this  kind. 


THREE-PART  DOUBLE   COUNTERPOINT. 


77 


§22.  If  it  be  desired  to  let  the  alto  and  bass  exchange  places,  the 
same  rules  must  be  observed  as  were  given  above  for  the  mutual 
inversion  of  soprano  and  alto.  Only  the  suspension  of  9  before  8  must 
never  occur,  like  that  between  bass  and  soprano,  for  such  suspensions 
result,  on  inversion,  in  transgressions  of  the  rules  governing  suspen- 
sions. Therefore,  do  not  write  : 


200. 

C.  f. 

@EE5f 

&  & 

.  1 

—  ^iz  \ 

9 

r  r 

/A^*4t 

i 

l.C/-tti*  /»     «    . 

sp 

"i 

i       J 

for  the  inversion  would  be  : 


J I 


f\         /'i              ^*^ 

*     « 

(en      I' 

'       2^-Tf 

—                               """-• 

f»\^&    \ 

29 

-^&  «  s  1 

i£x  +t  (/   ^ 

1  1  * 

And  the  following  suspension  is  quite  as  wrong : 


We  consequently  alter  the  counterpoint  in  the  alto  as  follows : 


2Ola. 


/L    Z  (I*                ^ 

ln\  !L_JD 

•* 

t/              ^ 

f          r 

i  '  —  i  —  i 

[<?)•*?-    /I*         r3 

& 

•  —  *  —  *~ 

^  fi  \  /    2: 

•  • 

78 


DOUBLE   COUNTERPOINT. 


The  example  under  No.  201  b  shows  the  cantus  firmus  in  the  alto. 
The  interval  between  the  two  lowest  parts  may  be  as  wide  as  two 
octaves. 


^=        .-  

_ 

tf\\             IP 

S^j 

—  j 

2OH. 

'  "T  r 

r 

/WA«±f                 . 

^^ 

-„ 

[Cy  •  Jf  u.    /  ]  *          j^ 

&^    • 

• 

S^X     TL     V  \J             ^ 

fnT       * 

I 

H  1 

=»x-l 

" 

,  1  — 



•           i 

5\ 

J 

4 

•y 

-6 

=^H  !  1  r-r-. 

'- 

•             OCX 

1 

^=#  —  «>  — 

—0  —  f  —  -^  —  ^  — 

f? 

—  <9  1 

A  cautious  introduction  of  the  fifth  of  the  major  or  minor  triad  is 
also  necessary  here.  It  is  well  to  introduce  this  interval  either  as  a 
mere  passing-note  (then  best  on  the  weak  beat),  or  duly  prepared,  so 
that  on  inversion  the  chord  of  the  \  may  not  enter  unprepared  on  the 
strong  beat.  Only  the  chord  of  the  \  derived  from  the  tonic  triad 
is  allowed  to  enter  free,  towards  tHe  close,  in  preparation  of  the 
closing  cadence.  In  Ex.  201,  measure  3,  the  fifth  of  the  dominant 
triad  (A-C$-E)  appears  on  the  fourth  beat  in  the  bass.  Here  the 
root  of  the  triad,  A,  entering  in  the  soprano  on  the  first  beat  and  sus- 
tained, serves  as  a  preparation  for  the  fifth,  which  is  a  passing-note. 
In  the  fourth  measure,  D  is  held  in  the  bass  from  the  first  beat  on- 
ward ;  on  the  fourth  beat  it  becomes  transiently,  through  the  influence 
of  the  passing-note  G  in  the  soprano,  the  fifth  of  the  subdominant 
triad  (G-B-D).  The  same  thing  happens  with  A  in  the  alto  in  the 
sixth  measure  of  the  same  example. 

Ex.  202,  inversion  of  soprano  and  bass,  shows  us  the  fifths  of  the 
triads  on  the  2nd  degree  (measure  2,  E-G-B),  on  the  sixth  degree 
(measure  4,  J5-JD-JFJJ1) ,  and  of  the  subdominant  triad  (measure  6, 
A-C$-E),  as  passing-notes  on  the  fourth  beat ;  root  and  third  of  each 
triad  are,  in  each  case,  also  present  in  other  parts.  The  above  remarks 
concerning  preparation  and  introduction  of  the  fifth  likewise  apply 
to  Ex.  207. 


THREE-PART  DOUBLE   COUNTERPOINT.  79 

An  Inversion  of  Bass  and  Soprano  may  be  effected  thus : 


202. 

c.  f. 


fnr    ^!y 

ff  0  — 

o 

22    •                            • 

1                              ^ 
1            | 

/WA«-*        , 

\L^-^  *""  1*          ^j^                              XU 

sy 

2                ^J 

^^^  U  ^  y 

F                *'              * 

gfUttf^a- 
rn^*    »       ^       « 

,  

J  U  1  '— 

=      1 

V.V  7                                              •             * 

•^ 

1 

fj 

•J    r    T  ~r 

1     '     I     r 

fe)-ffTT~ 

—  7^  

1 

^"^    TI        ^ 

This  is  the  first  manner  of  inversion  ;  the  bass  is  inverted  by  two 
octaves,  while  the  soprano  and  alto  remain. 


-<5 1 


=t=q: 


Second  manner  of  inversion  ;  the  bass  is  set  two  octaves  higher, 
the  soprano  one  octave  lower. 


2O4. 


XI       If/  *          "*" 

;  1  

^9>—  ^  

&  

EzEi  i  —  i 

•  J                           ^ 

"^ 

Z^5**      i 

1 

^*^                                                                                 ^ 

Ic^fe  —  "  — 

J 

1 

£S 

^L) 

1 

-r  r  r  f  * 

^ 

^~       ~  ^ 

f(*3l2      i 

-f  —  *     » 

s 

m        m        0 

1 

L^_}f_J  — 

-i  —  I  —  r 

^  1 

80 


DOUBLE   COUNTERPOINT. 


Third  manner  of  inversion ;  the  bass  is  set  one  octave  higher,  the 
soprano  one  octave  lower. 


2O5. 


m  =52 

« 

x^" 

•v 

f     f    t    r 

"f^  f"         *  1 

f-^ 

£Pl$7—  •  '  

~~*  i  1  

C  d 

K.B. 


"^v  1     —  1  3  j  — 

tT        -g- 

*  *     «: 

•^ 

Z^ 

^^^i»~           ~^  T  1*  — 

\  ffi  

~r  —  r  —  r  —  =~ 

1 

^^f^    11       1 

i-,. 

Should  we  prefer  to  avoid  the  transient  crossing  of  the  parts  at 
N.B.,  in  No.  205,  which,  however,  is  not  at  all  faulty,  we  can  change 
the  counterpoint  of  the  alto,  which  is  a  free  part. 


206. 


jfo—  S^B-  

— 

ik  j    i 

1    '    r   r 

—  "~ 

^••n  ^ 

, 

i 

• 

. 

In  all  these  illustrations  it  makes  no  difference  whatever  in  which 
part  the  cantus  firmus  is  set  originally.  All  the  exercises  are  to  be 
worked  out  in  strict  accordance  with  the  rules  given  above. 

In  simple  triple  time  (3/4  or  3/2),  the  rules  already  learned  for 
counterpoint  in  duple  time  hold  good.  To  render  the  matter  yet 


THREE-PART  DOUBLE   COUNTERPOINT. 


81 


clearer,  we  subjoin  another  illustration,  in  triple  time.  From  the 
foregoing,  and  also  from  the  following  examples,  the  student  will  per- 
ceive that  the  fifth  of  the  triad,  wherever  occurring,  is  cautiously 
introduced  in  such  a  way  that  no  chord  of  the  fourth  and  sixth,  of  un- 
pleasing  effect,  will  result  on  inversion.  This  point  must  also  be 
considered,  as  far  as  possible,  in  these  exercises. 


207. 


c.  f. 


r- 


— • — j 


-» = 1 — 

£ L M"-: 

b_! 


m 


^J     i    i — T^H 

zi='=e-jzr= 


r 


First  manner  of  inversion.     The  soprano  is  set  an  octave  lower, 
the  bass  and  alto  remaining. 


2O8 


:q*-1=i 
—i — « — -•- 


rr — ^^ — 


;3= 


^ 


-• — f- 


=t 


r    r 


P-^H— r j 

--p — f—*-&:r  j3 


m 


The  manner  of  inversion  remains  the  same,  when  the  alto  is  set 
an  octave  higher,  and  the  soprano  is  left  where  it  was. 


DOUBLE   COUNTERPOINT. 


Second  manner  of  inversion  ;  both  bass  and  alto  are  inverted  by 
an  octave,  while  the  soprano  remains. 


209.  < 


V    V  vl      ^                            *     m 

J       1 

SL  7  Sf? 

i?   • 

fnV  *^i                         • 

•            « 

HZ      '-«-     •  •             i*      r 

*           I 

^    r      t  r 

1                1 

f  r  r- 

:«  • 

ddb^J 

"^^         .     - 

/wy  u  o                 •     • 

21 

1                                1 

|gyr  U  Q      «  ; 
**s<ri-~A—          ~«^*  — 

-i  3 

tj 


-«"- . 


^y— r- 


— «>--- 


^ 


Third  manner  of  inversion.     The  bass  is  set  two  octaves  higher, 
the  soprano  one  octave  lower ;  the  alto  remains. 


210. 


-Hy-n— ^--- 


=»=3_ 


1 


^ 


-| P-J 


The  fourth  manner  of  inversion  is  exhibited  (to  avoid  crossing  of 
the  parts)  according  to  the  following  scheme ;  the  soprano  set  two 
octaves  lower,  the  bass  one  octave  higher,  and  the  alto  left  where  it 
was. 


THREE-PART  DOUBLE   COUNTERPOINT. 


83 


211. 


- — 0- 


Exercises. 


212. 


213. 


NOTE. — In  order  to  save  room,  Exs.  199,  and  also  201  a  and  207,  are  so  worked 
out,  that  they  can  be  utilized  not  only  in  the  original  position,  but  also  to  exhibit  the 
various  manners  of  inversion.  It  is  by  no  means  necessary,  however,  for  the  student  to 
do  the  same;  for  this  would  render  his  work  needlessly  difficult.  As  an  accompaniment 
to  the  two  invertible  parts  he  should  write,  in  each  exercise  in  all  its  various  forms,  a 
free  third  part,  which  is  not  to  be  transposed  in  the  several  inversions.  In  case  the 
range  of  the  voice-parts  should  be  overstepped  in  the  original  key,  either  on  inversion 
or  in  any  further  working-out  of  these  last  exercises,  the  exercise,  or  its  inversions, 
may  be  transposed  into  any  suitable  key. 


84 


FOUR-PART  DOUBLE   COUNTERPOINT. 


CHAPTER    VIII. 

Double  Counterpoint  in  the  Octave,   in  Four-part 

Writing. 

§23.  The  simplest  species  of  double  counterpoint  in  the  octave, 
in  four-part  writing,  is  that  in  which  the  movement  is  so  constructed 
that  the  tenor  and  soprano  can  be  mutually  inverted  by  an  octave. 
No  new  rules  are  needed  for  this  work  ;  those  already  given  in  §§  21 
and  22  should  be  followed.  Below  is  an  illustration,  in  which  a 
counterpoint  in  the  tenor  is  set  to  the  cantus  firmus  in  the  soprano  in 
such  a  way  that  the  two  parts  can  exchange  places.  Alto  and  bass 
may  be  regarded  as  free  parts. 


C.  f. 


In  the  inversion  the  tenor  takes   the  cantus  firmus,  while  the 
soprano  assumes  the  counterpoint  of  the  tenor. 


Inversion  of  No.  216. 


Cp. 

217. 

c.f. 


DOUBLE   COUNTERPOINT  IN  THE   OCTAVE. 


85 


ll 


:  -G>— = — 0- 

-  -I & F — I — 

J±=t=t=:t 


But  in  Ex.  216  those  parts  which  are  not  originally  assumed  to  be 
invertible,  are  also  written  according  to  the  rules  for  double  counter- 
point. Consequently,  besides  the  inversion  of  soprano  and  tenor 
exhibited  above,  the  alto  and  tenor,  alto  and  bass,  tenor  and  bass, 
and  bass  and  soprano,  are  all  mutually  invertible,  so  that  Ex.  216 
yields  five  further  inversions.  But  we  desire  to  say  explicitly,  that 
the  student  is  not  in  any  way  obliged  to  work  out  his  exercises  in  this 
manner,  for  it  would  give  him  a  great  deal  of  unnecessary  trouble.  It 
is  better,  at  first,  that  only  one  of  the  parts  should  be  set  to  the  cantus 
firmus  in  the  relation  of  double  counterpoint  in  the  octave.  The 
other,  non-invertible,  parts  are  to  be  treated  as  free  parts.  Then,  by 
setting  the  cantus  firmus  in  different  parts  in  turn,  he  can  work  out 
various  exercises,  in  which,  without  paying  the  slightest  attention  to 
the  invertibility  of  the  free  parts,  only  two  parts  are  to  be  written  so 
as  to  be  mutually  invertible.  The  student  should  practise  exercises 
of  this  description  in  the  order  shown  in  the  following  inversions  of 
Ex.  216.  From  the  inversions  the  student  will  notice  that  the  fifth  of 
the  triad  has  to  be  introduced  with  special  caution  wherever  the 
ensuing  inversion  brings  it  into  the  bass.  In  this  case,  too,  the  sus- 
pension of  9  before  8  can  hardly  ever  be  used.  In  fact,  the  prepara- 
tion and  resolution  of  suspensions  must  be  most  carefully  considered 
in  these  exercises.  The  employment  of  the  augmented  sixth  will 
probably  be  attended  with  equal  difficulty.  This  interval  becomes, 
on  inversion,  a  diminished  third,  which  is  not  only  harshly  dissonant, 
but  is  also  apt  to  occasion  faulty  progressions  ;  e.g., 


Inversion. 


Inversion. 


86  FOUR-PART  DOUBLE   COUNTERPOINT. 

Avoid,  therefore,  the  employment  of  the  augmented  sixth  both  in 
the  chords  of  the  augmented  fifth  and  sixth,  and  of  the  third,  fourth, 
and  sixth.  The  augmented  fifth  may  be  occasionally  employed,  as 
shown  in  Ex.  216,  measure  5. 

We  now  give  below  the  inversions  of  other  pairs  of  parts,  exhib- 
ited by  further  transpositions  of  Ex.  216. 

1.  The  cantus  firmus  in  the  alto ;  the  soprano  takes  the  coun- 
terpoint of  the  alto ;  to  facilitate  singing,  this  inversion  is 
transposed  into  F  major.  As  mentioned  before,  such 
transpositions  into  other  keys  are  often  rendered  necessary 
by  certain  inversions,  so  as  to  keep  the  parts  within  the 
range  of  the  voices. 


218.  ( 


2.  The  cantus  firmus  in  the  soprano ;  the  alto  takes  the  coun- 
terpoint of  the  tenor,  the  tenor  that  of  the  alto.  The  in- 
version is  transposed,  for  the  reasons  given,  into  A  major. 


219. 


DOUBLE   COUNTERPOINT  IN  THE   OCTAVE. 
Ta^H — *~ 

-9— g 

— ^ — h 

i — r 


«-» i .- — I 1 1 1 

«*[•— g| >"=—  =  -V.    I        & g) 1-  — 


m 


-•& •*— 


AJ_J 


3.  The  cantus  firmus  in  the  soprano ;   the  alto  takes  the  coun- 
terpoint of  the  bass,  the  bass  that  of  the  alto. 


22O. 


— <&--- 


-2 7? (• 


1 


25* 


P 


^J,g      _m          ^ 


-f— f— f2-! 

:e=t:=t— ' 


4.  The  cantus  firmus  in  the  soprano  ;  the  tenor  takes  the  coun- 
terpoint of  the  bass,  the  bass  that  of  the  tenor. 


221. 


:3=zz: 

^= 


-4—4- 

=^:J — &—- 


-& — -^ — »9- 


2_ fe^  =«_»_|_^ g ^I*_ 


FOUR- PART  DOUBLE   COUNTERPOINT. 

5.  The  cantus  firmus  in  the  bass ;  the  soprano  takes  the  coun- 
terpoint of  the  bass. 


222. 


O' 

<=/  .                      i 

Kx 

a__ 

xs                             m 

v4y        —  ^,       *^    if'**' 

5_ 

1        *  '  •     P      • 

Er~~r~1     1 
-«•-      -•-  , 

iji-  — 

r  '  »  i    i  rr 

"   i 

'-^         x-j 

*                    i 

i^/«      '^ 

1       f55 

<j                     \ 

k^  ^/                   ^^ 

^  •           &  • 

I2    !       1 

• 

In  like  manner  other  inversions  are  to  be  worked  out;  for  in- 
stance, the  mutual  inversion  of  bass  and  alto  when  the  cantus  firmus 
is  in  the  tenor  ;  of  bass  and  soprano  when  the  cantus  firmus  is  in  the 
alto  or  tenor  ;  etc.,  etc. 

The  student  should  work  out  the  next-following  exercises,  to  begin 
with,  as  simply  as  possible  in  equal  counterpoint ;  after  which  he  may 
attempt  to  write  a  figurate  counterpoint,  to  the  same  cantus  firmus,  in 
the  part  to  be  inverted  and  also  in  the  free  parts.  The  student's  own 
practical  work  will  gradually  render  the  foregoing  rules,  laws,  and 
observations  touching  this  species  of  double  counterpoint  quite  clear 
to  his  mind.  The  inversion  of  each  exercise  ought  regularly  to  be 
written  out  in  full,  so  that  the  student  may  accurately  comprehend 
the  effect  of  his  work  in  its  dual  development.  Under  certain  condi- 
tions an  examination  of  the  inversions  may  lead  to  various  alterations 
in  the  original  work.  And,  above  all,  the  student  should  see  to  it, 
that  each  individual  part  has  an  independent  melodic  leading,  and 
that  the  interval  between  the  various  parts  remains  within  the  bounds 
prescribed  for  the  inversions  to  be  made. 


Exercises. 

The  cantus  firmus  may  be  given  to  any  part;  the  manner  of 
working  out,  with  two  free  parts,  is  exhibited  in  the  following  exam- 
ples, the  cantus  firmus  being  that  given  under  No.  224. 


DOUBLE   COUNTERPOINT  IN  THE    OCTAVE. 


89 


1.  The  cantus  firmus  in  the  soprano,  counterpoint  in  the  tenor. 
Alto  and  bass  are  free  parts. 


223  a. 


<u 


Inversion. 


j 

1    -J- 

' 

rt 

| 

1        1      J 

L         *^      w 

J 

_ 

m      fj  i 

^L           \ 

^w         *& 

^t 

f 

«  * 

™ 

^              _'             ^ 

l/"pv 

^—  ^ 

—  j        ' 

S3Z 

_ 

[^ 

^J 

v  

fffff 

\         i     1 
-J-       -*-  — 

A- 

i 

J. 

I 

•     -0-       j 

-&- 

y^A« 

_ 

l^L'* 

i      *    • 

*^MJ/                  'V 

0 

^                               ^ 

& 

^ 

-     •  •  ? 

~*.    f           j 

1       ^ 

i                I 

2.  Cantus  firmus  in  alto,  counterpoint  in  soprano.     Tenor  and 
bass  are  free. 


2236. 


=t 


tt 


flj    ^^ 


Inversion. 


.     !      •   J    J-rJ.  J-H^ .'       '      I      I    -I 

^r~~rf[  -^-rtg^^jj^r3 

—fi> — L4-—      L L*     i  j  L * 1  i      i  i  !•-*• 


1 


^: 


90 


FOUR-PART  DOUBLE   COUNTERPOINT. 


3.  Cantus  finnus  in  soprano ;    the  inner  parts  are  mutually 
inverted. 


223  c. 


E=g^f=f=Ef- 


± J- 


W 


& 


i  J 

^  Efr      ~ 


Inversion. 


*'=, 


etc. 


m 


4.  Cantus  firmus  in  soprano ;  tenor  and  bass  mutually  invertible. 


223d. 


J(  fa  —  557  •  

—  ±1  —  *  5  — 

m 

LTk\U                  1^1 

-^ 

m                        g 

\A)    '         N»        ^     • 

•^ 

•           ' 

1            |                    ^$L       etc. 
JSL  -                      ...'  ^ 

y^\«                                             — 

L^r  "*/    ^                                                  j  |                   ^ 

^-X\    /           XJ,                                I                   1          tf 

.    m                   m        t  .  ... 

Inversion. 

1 

J                                                      1       ' 

.i 

JT                                -I 

2    •                      • 

•        1 

9^m                        ^^ 

I*          /•? 

\(\\                       **                        «<? 

•                     il 

v^jy          **»           2_      * 

1 

i- 

A 

L        £ 

J     i    J    J 

f                      1 

_J_   ^                     J^etc. 

(m)' 

a  f2  1 

^         ^          f    ^ 

t                   * 

^     •                           2 

-*  —  r 

•»^_ 

-^ 

DOUBLE   COUNTERPOINT  IN  THE   OCTAVE. 


91 


223  e. 


5. 

Cantus  firmus  in  bass  ;  bass  and  so 

prano  mutually  inverted. 

Jr     1           J                i       L 

1 

i  

H  •       • 

-*    H 

/pf\  (1*  ^  —     —  •'  1?*  — 

—  9—  B*  —  -  —  r- 

T  — 

V>ly              K 

r 

i)                -«^_ 

pf  r  r 

i 

1 

J.    , 

t  JU- 

h     ^* 

^ 

I 

ZSv  ,                            4          * 

&) 

^y     *                                  ^ 

If*/*        ^                           * 

0 

r    _i 

<~sl\J              X3                           P 

Inversion. 


•  ± 


E^E^ 


-i — r 


-s=^ 


a 

<s>  • 

i 

0  —  1 

i 

i  m  1  

—  y.  

i/^v 

( 

i*I}                                                            ' 

rz           1 

^s'L' 

£         1 

n 

^m^mfm^ 

etc. 

^-         ±:  -i    -J-^    " 

^-T  j  j  ^     ^ 

^ 

/^\* 

»   •  *              m 

i 

L^L'* 

«     • 

i                         i           m                 m 

1 

^—  ^ 

•           •    i       i 

\,                           * 

^5 

Exercises. 


225. 


226. 


227. 


zrzH 

_ 

-& 

rrhv-1     _, 

*j 

^ 

1 

92  TRIPLE    COUNTERPOINT. 


OBSERVATIONS  ON  THESE  EXERCISES. 

It  makes  no  difference,  if  one  of  these  inversions  happens  to  begin  or  close  on  a 
chord  of  the  sixth;  but  the  chord  of  the  fourth  and  sixth  should  not  occur  at  either 
beginning  or  close.  Remember  also,  in  the  midst  of  an  exercise,  what  was  said  above 
concerning  the  introduction  of  the  fifth  of  the  triad,  which,  when  inverted  into  the 
bass,  forms  a  chord  of  the  fourth  and  sixth.  Of  course,  this  chord  is  not  to  be  wholly 
avoided;  the  student  must  not  suppose  that  it  is  absolutely  inadmissible  anywhere  and 
everywhere.  He  must  only  take  care,  wherever  the  chord  occurs,  that  it  enters  in  a 
proper  and  fitting  manner,  for  it  would  otherwise  sound  weak  and  have  a  bad  effect. 


CHAPTER    IX. 

Triple  Counterpoint  in  the  Octave,  in  Three  and 
Four-part  Writing. 

§24.  When  all  the  parts  have  been  written,  in  a  three-part  move- 
ment, according  to  the  rules  already  learned  for  double  counterpoint, 
five  different  inversions  can  be  made,  as  tabulated  below : 

1st  Position.  2nd  Position.  3rd  Position.  4th  Position.  5th  Position.  6th  Position. 

1.  Soprano.  1.  Soprano.  2.  Alto.  2.  Alto.  3.  Tenor.  3.  Tenor. 

2.  Alto.  3.  Tenor.  1.  Soprano.  3.  Tenor.  1.  Soprano.  2.  Alto. 

3.  Tenor.  2.  Alto.  3.  Tenor.  1.  Soprano.  2.  Alto.  1.  Soprano. 

In  these  inversions,  in  order  to  prevent  an  awkward  crossing  of 
the  parts,  one  part  or  another  may  be  inverted  by  two  octaves  when 
the  effect  is  good.  In  ordinary  inversion  by  one  octave,  it  does  no 
harm  if  a  lower  part  crosses  an  upper  part  for  a  few  notes,  occasion- 
ally ;  but  this  must  not  continue  through  several  successive  measures, 
because  then  the  effect  of  the  inversion  would  be  nullified.  And  no 
other  part  is  permitted  below  the  bass  (or  the  lowest  part) ,  in  any  in- 
version whatever,  either  momentarily  or  with  several  successive  notes. 
At  beginning  and  close,  the  fifth  of  the  triad  is  to  be  avoided,  so  that 
none  of  the  inversions  shall  begin  or  end  on  the  chord  of  the  fourth 
and  sixth ;  in  the  midst  of  the  exercise,  too,  all  previous  rules  and 
remarks  on  the  position  and  entrance  of  that  chord  are  to  be  observed. 
The  suspension  of  9  before  8  must  always  be  avoided.  The  leading 
of  each  part  should  be  melodically  independent ;  for  each,  when  set  in 
the  soprano,  becomes  most  prominent.  For  this  reason  the  long  con- 


THREE-PART  TRIPLE   COUNTERPOINT. 


93 


tinuance  of  a  part  on  one  tone  is  not  allowed,  except  in  case  a  sus- 
tained tone  (organ-point)  is  intentionally  written.  But  the  effect 
would  not  be  particularly  good  in  three-part  writing. 

Below  is  given  an  illustration  of  this  kind  of  triple  counterpoint, 
with  all  the  inversions.  The  cantus  firmus  is  first  set  in  the  bass ; 
this  example  also  shows  how  the  fifth  of  the  triad  can  be  introduced. 


/ 

7T-7    TV     - 

9^ 

»  •  •     *?« 

2.             / 

Prv   vfr   ^ 

->       -                      1 

J      *up            r*f  i 

m       m         »    m 

228. 

X  -r  1 
1 

'    f    i 

(•       i         i 

\    i     L 

I 

ZJp     k      1              0 

-•  £    1-  t  i  —  L_i 

=^—              — 

\ 

2CS    ^         M    - 

im        •        *j*      « 

1   (g%> 

SS2                   S* 

^•^ 

• 

— 

' 

t/           ^ 

* 

„* 

" 

0- 

gr 

-^ 

'*"    + 

. 

1 

1 

S3 

^^ 

™ 

_ 

(^\*    IT 

. 

/^ 

I 

l^^*l    P 

%  —  '\y 

1 

As  in  Examples  201,  202,  and  207,  it  will  be  seen  that  the  fifth  oi 
any  major  or  minor  triad  is  carefully  prepared.  Only  in  the  last 
measure  but  one  does  the  fifth  jP,  in  the  bass,  enter  free  on  the  first 
beat.  But  in  this  case  it  is  the  fifth  of  the  tonic  triad,  and  just  before 
the  close ;  the  resulting  chord  of  the  fourth  and  sixth  is  in  its  proper 
place,  and  is  peculiarly  adapted  to  give  the  impression  of  an  ending, 
and  to  prepare  the  close;  besides,  the  root  of  the  triad  (B*7  in  the 
alto)  is  prepared. 


TRIPLE    COUNTERPOINT. 


First  inversion.      The  alto  is  set  an  octave  lower,  taking  the 
lowest  part. 


3. 

229. 


'• 


i — k. 

>    i/     • 


-*— 


atr 


rrr~r 


EEE 


*c 


Jf  I/-"-  1      —  ^  — 

i 
1 

KTr        *        VvJ     0 

5SJ2                   *Jt^ 

M         *                            tf 

! 

i 

W                -Z7-                                    * 

T  f  F 

i     i 

cH  1  1  1 

f  ^  r  f 

^-b—  ^  

=^  '  •]  

-^-i 

Second  inversion.  The  alto  is  set  an  octave  higher,  and  takes 
the  highest  part.  To  be  sung,  these  examples  would  have  to  be 
transposed  into  O  J  major. 


i. 
23O. 


y= 


£i 


THREE-PART  TRIPLE   COUNTERPOINT. 


95 


u 


=s 


*         fy 

—  &—  —  j— 

--fi»        | 

<^  —  f  —  r&»~~*~~ 

^~'  *~ 

1 

gr-  *1      gpi      * 

1                       ^ 

r     r 

TBT 

.   .                «7 

fW-H*  

^-*—r—&  —  | 

1    »  *  E       t 

T^—  1 

^^^  

^-  1 

Third  inversion.     The  soprano  is  set  an  octave  lower,  the  bass 
and  alto  an  octave  higher ;  the  soprano  now  takes  the  lowest  part. 


231. 


Jbs=±=r-tt=t&=\ 


=t=t 

•^••k 


, ,-Q*— £l- fe*_. 

— U*=E=E=I 


«       -»-  L 

—•?+-    zzfee: 


•^   T    j 


S 


t=t 


E^S 


-f- 


^r  K         ".^-i 

2                             J 

iCn           ^  ^ 

& 

r  •  •  s— 

S2 

1  1  1  

tp  —  i  •  —  P—  J 

i     '     r    i 
i 

fi*)"  h>    '         *C*    ' 

n^ 

^J  —  1—      ^_  —        * 

—  i  v  — 

** 

TRIPLE   COUNTERPOINT. 


Fourth  inversion.     The  bass  is  set  an  octave  higher ;   in  this  in- 
version the  alto  takes  the  lowest  part. 


3. 

i. 
232. 

2. 


N^u? 


:q=: 


=4: 


:d: 


:=i: 


Fifth  inversion.  The  bass  is  set  an  octave  higher,  the  soprano 
an  octave  lower.  The  bass  takes  the  highest  part,  the  soprano  the 
lowest. 


3. 

2. 

233. 
i. 


-4- 


-•— <2—   -J-* * 

|        I  |  I 


-- *- 


.FOUR-PART   TRIPLE     COUNTERPOINT.  97 

===M=±=& 


tsU^^tJ^ 


Exercises. 


234. 


236. 


After  the  student  has  worked  out  each  of  the  above  exercises,  let 
him  try  to  invent  similar  three-part  examples,  admitting  of  five  inver- 
sions, by  himself. 

If  it  be  desired,  in  a  four-part  movement,  to  set  the  three  highest 
parts  in  triple  counterpoint  in  the  octave  to  the  cantus  firmus,  we  shall 
find  this  task  even  easier,  in  various  ways,  than  the  foregoing  three- 
part  exercises.  As  none  of  the  three  highest  parts  has  to  be  inverted 
at  any  time  so  as  to  become  the  bass,  the  fifth  of  the  triad  can  be 
employed  unrestrictedly.  And  even  the  suspension  of  the  ninth 
before  the  octave  can  be  employed,  under  certain  circumstances,  as  we 
shall  show  directly  in  the  following  example  (measures  5  and  7).  An 
occasional  transient  crossing  of  the  parts  in  one  of  the  five  inversions, 
is  a  matter  of  no  importance,  particularly  in  the  inner  parts.  Some 
of  the  inversions  would,  of  course,  have  to  be  transposed,  if  they  were 
to  be  sung. 


TRIPLE   COUNTERPOINT: 
The  cantus  firmus  is  in  the  Bass. 


237,  < 

3. 
C.  f. 

npW~*~              - 

^^-J-S^ 

m                 m 

i 

•  F— 
1             1 

e       -*• 

•^    1                  1 

^                 J 

-1  ' 

1 

jO- 

I 

PV^L  t  * 

{*-* 

2 

^^P-^K  

A  crossing  of  the  parts  in  any  of  the  inversions  can,  of  course, 
occur  only  when,  in  the  original  position,  one  of  the  higher  parts  to 
be  inverted  was  at  an  interval  of  more  than  an  octave  from  the  other, 
as  is  the  case  between  the  tenor  and  alto  in  Ex.  237,  measure  3.  From 
the  leading  of  the  soprano  in  measure  2  it  will  be  seen,  that  the  altered 
fifth  may  very  properly  be  employed. 

First  inversion,  transposed  into  (7  major. 


£L  11*      f 

*         f         *      Jt* 

ex 

frnV'                           » 

s-j        w 

^                      « 

S2   '        N»        f     -  f        f 

^ 

&     *    f    i     r 

'1             I      ^ 
i     i  , 

238. 

2. 

J.  J.  J  * 

_<2-       . 

i  J  ^ 

{f*)'/lt  

O.  f. 

^-^\b 

FOUR-PART  TRIPLE   COUNTERPOINT. 
Second  inversion. 


99 


2. 
1. 

239. 

3. 

C.  f. 


-1 — -f 


J-J. 


s 


EEF 


Third  inversion,  transposed  into  D  major. 


2. 
3. 

240. 


c.  f. 


\J  *T||    I             V»             f 

•       • 

V 

(5x~*(|v      v.                     i          m 

b^         • 

\^LL  !^  «  1  

tT                 |       I 

^  1 

1  r 

J-  Jsi    * 

JO.. 

f^\"*      1 

l^'-*f>/i     .- 

^-/.  SJE     2 

sy 

%±± 


-&--- 


tfUA. 


r 


Fourth  inversion. 


3. 

2. 
241. 


c.  f. 


ZIHflE     ^        J        « 

» 

z 

•         *    • 

^Kpip.  .<*  ...>.  ; 

P 

X 

=^H  •  1  N»'  

^(Z  f  

v                   1 

E^  j  1  1  1 

.a. 

"-*-  J-  Aiu 

= 

/^\»        J-            ^3 

L  ^y  •(    /  1  1        ^^ 

-_ 

s? 

V^|jlJ2  

—  ^  

100 


TRIPLE   COUNTERPOINT. 


Fifth  inversion. 


242. 

2. 
C.  f. 


— *- 


-tf- 


-J       !     J.     J 


rf"u    : 

1 

^=^ 

=^r- 

1  

i  —  Mn 

r—  |  

—  h 

-75  1 

d^  —  i 

• 

9 

—  -  —  • 

— 

s 

3= 

^3 

?-  • 

(2 

?          • 

r 

;• 

1  ^  • 

°  r 

£V      f 

5        • 

T 

^r 

•    • 

^*^         A 

PA     E 

• 

• 

-~* 

I 

^h 

r^     - 

2 

Exercises. 


243. 


244. 


QUADRUPLE   COUNTERPOINT  IN  THE   OCTAVE.  101 


Quadruple  Counterpoint  in  the  Octave. 

§25.  In  this  species  of  counterpoint,  the  four  parts  must  be 
capable  of  presentation  in  23  inversions,  i.  e.,  including  the  original 
position,  in  24  different  forms.  In  the  scheme  below,  the  soprano, 
alto,  tenor  and  bass  are  represented,  for  the  sake  of  brevity,  by  the 
figures  1,  2,  3  and  4,  respectively. 


111111 

223344 
342432 
434223 

222222 
113344 
341431 
434113 

333333 
112244 
241412 
424121 

444444 
112233 
231312 
323121 

In  this  case,  too,  no  new  rules  have  to  be  formulated.  But  the 
strictest  observance  of  all  the  restrictions  hitherto  required  in  double 
counterpoint,  is  necessary  for  the  mutual  relations  of  all  four  parts, 
if  the  inversions  are  to  turn  out  well.  In  practical  composition,  such 
movements,  capable  of  ^affording  23  inversions,  are  seldom  required. 
And  in  no  case  would  all  24  positions,  however  good  their  effect  might 
be,  appear  in  one  and  the  same  composition.  This  would  only  pro- 
duce monotony.  We  therefore  advise,  that  work  in  this  species  of 
counterpoint  be  not  too  prolonged.  On  the  other  hand,  we  urgently 
recommend  exercises  in  triple  counterpoint ;  for  such  movements — as 
we  shall  see  later  in  the  study  of  the  fugue — very  frequently  occur  in 
practice. 

An  illustration  in  quadruple  counterpoint  follows.  Of  the  24 
positions,  we  shall  here  take  note  of  only  the  four  principal  ones ; 
these  being  the  inversions  in  which  each  part  changes  its  place  each 
time. 

1234 
2143 
3412 
4321 

The  student  may  write  out  the  remaining  inversions  himself  ;  he 
will  perceive,  that  when  the  parts  are  set,  in  their  mutual  relations, 
according  to  the  rules  for  double  counterpoint,  the  inversions  will  all 
be  good.  Ex.  216  is  also  worked  out  in  quadruple  counterpoint ;  the 
student  may  write  out  the  17  possible  inversions  remaining  after  the 
six  inversions  given  below  under  Nos.  217-222. 


102 


QUADRUPLE   COUNTERPOINT. 


1. 

2. 

2456. 

3. 

n    u                     — 

*                  h 

/L  b  /  * 

-^  —  d  —  e  —  *— 

"iP5  

(3>      5^—  £  *-     *  • 

^  *  •  *  m  •  *\ 

j        r  i  i 

C.  f. 

"  —  ^~l£lj 
J  J- 

N» 

/-""^*   '-I  ..                        _ 

ICA  !//*                   ™ 

^* 

» 

^^b  «•  J                 _ 

Here,  too,  the  preparation  of  the  fifth  of  the  major  and  minor 
triad  is  carefully  provided  for  in  all  the  parts ;  only  on  the  third  beat 
of  the  eighth  measure  do  we  find  the  fifth  of  the  triad  on  the  2nd 
degree  (C—Efy—Gf)  entering  free  as  a  passing-note.  In  the  inversion 
(Ex.  245  c)  the  effect  is  by  no  means  bad,  this  fifth  being  a  chromatic 
and  unessential  passing-note.  This  leading  might  easily  have  been 
avoided  ;  it  was  written  intentionally,  in  order  that  this  exceptional 
case  might  also  be  treated  in  the  course  of  instruction. 


245  c. 

4. 
3. 


fg        i»       J  J  J 

^ 

^j 

—  *  9—A-0  —  t-j-*-i 



•  0-m 

^ 

5f      •      •  —  F 

—&  

L         1  F—  t—  ' 

-f-    -0- 

/jj"N«jt                                   ^ 

M 

~  1  F  —  | 

(£^^(-7- 

-*  —  f— 

QUADRUPLE   COUNTERPOINT  IN  THE   OCTAVE.  103 


J 


i  I  r 


ffi 


==  =?CppEU-|»  -  » 


3. 

4. 

245  d. 
i. 

2. 


yr  h  /»                ™ 

s» 

'1 

frr\^  *  ' 

^5 

•  — 

tJ 

---                  *      J     -J- 

^    .-^ 

?"  •      •          • 

(/•V    1                          9          *          \ 

^ 

=^1  — 

^**-t7     *  .  1  ^— 

-  **^^^-h- 

n  ^ 

-- 


±  •*  J. 


j-, 


i  ^ 


r   -r    TTn 


104 


QUADRUPLE   COUNTERPOINT. 


245  e. 

2. 
1. 


I        1     - 


JT*=tM+ 


Below  we  also  give  Ex.  216  in  the  inversion  I . 

i 


245 /. 


ai^-fg-T 


?fi— 

^^     g  5  

^ 

• 

^T^  

6> 

^             'i 

—(2  

»   ^ 

1 

cr 

,            , 

1 
J 

! 

^-1  — 
1 

\     '     1 

1 

fit)' 

H              C'       ]f^ 

^ 

3 

2 

^ 

i   *   • 

9       •       M            1 

c^ 

2 

—  >s  —  ' 

— 

s  

<s>- 

...    —  0 

^S^^E 

247. 


DOUBLE    COUNTERPOINT  IN  THE    TENTH.  105 

Exercises. 


35E      *    MSF-f-E-'-tif  |«^ 


4£>'(*— 

XQ 

-si 

-T—  •— 

-»  *  •— 

-i- 

248. 


gj£f??^ 


It  is  also  good  practice  for  the  student  to  invent  original  exercises 
worked  out  in  quadruple  counterpoint. 


CHAPTEK    X. 
Double  Counterpoint  in  the  Tenth  and  Twelfth. 

§26.  For  double  counterpoint  in  the  tenth,  one  part  must  be 
written  which  is  invertible  by  a  tenth  (or  third).  The  intervals 
yielded  by  the  inversion,  may  be  exhibited  by  the  following  series  of 

figures : 

1.    2.    3.    4.    5.     6.    7.    8.    9.     10. 

10.    9.    8.    7.    6.    5.    4.    3.    2.      1. 

It  is  self-evident,  that  in  this  kind  of  counterpoint  two  thirds  (or 
tenths)  or  two  sixths  cannot  follow  in  succession ;  for  on  inversion 
they  would  result  in  parallel  octaves,  unisons,  or  fifths. 


Inversion. 


106 


DOUBLE   COUNTERPOINT  IN  THE    TENTH. 


Fourths  and  sevenths  can  be  employed  only  as  passing-notes, 
and  when  the  fourth  is  led  into  the  fifth,  the  seventh  into  the  sixth ; 
e-  g., 


Inversion. 


Inversion. 


3C-3C      1                     i               1                           w 

*-  - 

m     J-.          •     •  -    «  .          • 

'        | 

J     s  r  r  T  ^ 

yilj  «  j  j  j_ 

L1  ' 

/i  1*TT                                                                      2 

J                  • 

i^y»i»              __      •                                 ^                                           -_      •                                   A 

^ 

*^M-/'    *5       ^*^                                                                  i^                                 ; 

'                     | 

^                                1 

n         1     1     i      i          -'  •          ' 

a 

V     >•    <t                            i                               i 

_  i 

/L      *             *     h»                \ 

i 

rh                           •     1 

i 

532                             •        •       '                               «     1 

•     i 

d         (»    •                                                           (2?    ' 
1                                    1 

^*     «                   n 

i 

^*                 i       •       •      1  V 

t    i 

i^x      ^*                          1            1          1/rU    X      h     -  *     ^ 

j    i 

• 

The  suspended  ninth  is  resolved  as  follows : 


Inversions. 


^1=^^ 


JS-  .(2- 


±± 


i« 

fls 

• 

S3Z 

5* 

*  i 

^^ 

«J       .» 
1 

"  "^r  ^ 

r  ' 

^                       m 

•v. 

fW*  ' 

*    i~tr  za 

*        <^> 

• 

t 

•         2 

« 

Si 

^^  

_j^ 

^f  1 

It  is  clear  that  we  can  employ,  in  double  counterpoint  in  the 
tenth,  only  contrary  and  oblique  motion  ;  because  the  intervals  which 
are  employed  in  parallel  motion,  namely,  consecutive  thirds,  sixths, 
and  tenths,  must  here  be  excluded. 


DOUBLE   COUNTERPOINT  IN  THE    TENTH. 


107 


Earlier  text-books  lay  down  a  very  considerable  number  of  further 
rules  for  the  successions  of  intervals,  the  suspensions,  and  the  pro- 
gressions, which  are  to  be  avoided  or  allowed.  All  these  rules  are 
unquestionably  correct ;  but  they  serve  chiefly —  as  we  know  from 
many  years'  experience  in  teaching — to  confuse  the  pupil.  We  lay 
down  only  a  single  rule  for  double  counterpoint  in  the  tenth  ;  it  con- 
tains everything  needful  for  writing  such  counterpoint : 

In  setting  a  lower  part  to  a  higher,  write  the  lower  part  in  such 

a  way  that  it  may  be  accompanied  throughout  by  the  Third 

above. 
Or,  in  setting  a  higher  part  to  a  lower,  write  the  higher  part  in 

such  a  way  that  it  may  be  accompanied  throughout  by  the 

Third  below. 

Then,  if  we  have  observed  the  rules  for  double  counterpoint  in 
the  octave,  the  parts  of  a  movement  written  as  described  above  can  be 
inverted  by  a  tenth. 

Examine  the  following  little  example : 


To  the  cantus  firmus  in  the  higher  part,  the  lower  part  has  been 
set  in  such  a  manner  that  we  can  either  add  the  lower  third  to  the 
higher  part  or  the  higher  third  to  the  lower  part.  The  parts  being 
written  according  to  the  rules  for  double  counterpoint  in  the  octave, 
we  can  now  invert  either  part  by  a  tenth,  or,— what  amounts  to  the 
same  thing — -by  a  third.  This  is  illustrated  in  the  following  ex- 
amples : 


108 


DOUBLE   COUNTERPOINT  IN   THE    TENTH. 


First  manner  of  inversion.     The  higher  part  is  set  a  tenth  (or 
a  third)  lower ;  the  lower  part  remains. 


250. 


-*-?£- 


(g=^g=F-z==i^g-f"^rf^ 
i — i^ 1 — i  1 1 — ^^^i_ 


Of  course,  one  or  two  free  parts  are  to  be  set  to  this  inversion, 
and  also  to  those  following.  Two-part  counterpoint  of  this  sort  is 
not  employed  in  practical  work. 

Second  manner  of  inversion.  The  higher  part  remains  ;  the  lower 
is  inverted  by  a  tenth  (or  a  third)  higher. 


251. 


it: 


DOUBLE  COUNTERPOINT  IN   THE    TENTH. 


109 


Third  manner  of  inversion.      Both  parts  are  set  a  third  (or  a 
tenth)  higher. 


252. 


^(2.  -<9- 

=£= I— 


n=p;-gj — p — g=pr=^^ 


Fourth  manner  of  inversion.    The  higher  part  is  set  a  tenth  lower, 
the  other  a  tenth  higher. 


253  a.    < 


-(2- 


With  three  parts,  the  example  assumes  the  following  forms,  the 
added  third  part  being  written  in  double  counterpoint  in  the  octave. 
Here  only  the  beginnings  are  written  out ;  the  student,  for  better  com- 


110 


DOUBLE    COUNTERPOINT  IN  THE    TENTH, 


prehension  of  the  matter,  may  write  out  the  entire  example,  and  all 
its  inversions,  in  full. 

First  mode. 


2536. 


Second  mode. 


253  c. 


But  we  might  add,  instead,  a  third  part  not  invertible  (not  in 
double  counterpoint  in  the  octave) ;  in  this  case  the  third  part  has  to 
be  rewritten  to  fit  each  new  inversion  of  the  parts  in  counterpoint, 
as  an  inner  or  a  lowest  part.  We  might  also  add  two  free  parts  to  the 
two  original  ones  in  double  counterpoint  in  the  tenth,  which  free  parts 
would  have  to  be  remodelled  for  each  successive  inversion.  To  illus- 
trate, we  give  Ex.  250  (the  first  inversion  of  No.  249)  with  one  free 
part  (in  the  soprano) ;  and,  in  Ex.  253  a  in  the  fourth  inversion,  with 
two  free  parts  (soprano  and  tenor). 


25== 

\—  r  1  

1  ' 

1  

.  _H  

0 

i  —  1 

9 

1 

I  \ 

DOUBLE   COUNTERPOINT  IN  THE    TENTH. 


Ill 


Here  the  inversion  of  253  a  is  given  transposed  into  A  minor,  thus 
bringing  it  within  the  compass  of  the  voices. 


253  e. 


^ 


-^-rf-g  ^2 


fe— =t^3=4=t 
^E— &-  —•&-*- 


is 


r?  «-»-^- 


5££? 


^= 


^ 


-•-r 


I^SE  E£ 


§5 


d     •  I    0-     J      I  I 1 \ 

— $**—*          Jfr^       *          J 


112 


DOUBLE   COUNTERPOINT  IN   THE    TENTH. 


It  is  self-evident  that  this  species  of  double  counterpoint  may  also 
be  written  in  four  parts,  by  combining  the  two  modes  of  presenting  it 
in  three  parts;  e.  g., 


254. 


This  was  previously  suggested  in  Ex.  249  by  means  of  small 
notes  ;  here  we  give  three  inversions  of  the  example.  In  doing  so  we 
arrive  at  the  conclusion,  that  there  is  no  other  species  of  triple  and 
quadruple  counterpoint  besides  that  in  the  octave. 


255.  / 


k-^-£^ rj-  'a  J      ij^NSL 

|g^^-f=4f---g'-r-==1^=^gEl 

1  ^         '  '  "^  BM^BH  ^^*^*l 


ii==^=i=ss 


=t* 


:t= 


r: ^_«. 

•*-=-*-! H 


SE^fe 


±1=533=101 

W^ 


-g- 


rt=t=l 


256. 


DOUBLE   COUNTERPOINT  /N  THE    TENTH. 


113 


tFf^ 

-p-F-»-£- 


i=g: 


=£ 


r=* 


2 


1 


257. 


J5 


r--— i aj-4 

h=-!=3E; 


-i.-^ — ^ 


-(=2- 


t=T=piad 


£-1  p  L  r-p-T^ 


1 — • — i — i — i- 
5=j— r~F 


fc-P 


i    i     i    i  T^      i        ,^n      i    i 
•  •  -  y  •  '  •  -  •  *^  J-p-7- 


We  also  subjoin  an  illustration  of  the  employment  of  this  species 
of  double  counterpoint ;  this  is  the  Stretto  from  Bach's  Bb  minor 
fugue,  in  Part  II  of  the  "  Well-tempered  Clavichord." 


258. 


5^ 


•gjp     ^  J-qy— rfi=^=| 

EP  t=S=d 


= 


114 


DOUBLE   COUNTERPOINT  IN   THE   TWELFTH. 


If  the  student,  in  the  first  two  measures  of  this  example,  will  set 
the  first  six  notes  in  the  soprano  an  octave  lower,  he  will  obtain  an 
illustration  of  double  counterpoint  in  the  tenth,  formed  like  the  one 
in  No.  249. 

The  student  should  now  attempt  to  invent  exercises  in  double 
counterpoint  in  the  tenth  for  himself. 


Double  Counterpoint  in  the  Twelfth. 

§27.  An  examination  of  the  following  table  of  notes  and  the  ac- 
companying figures  shows  that  Prime  and  Octave  are  changed,  by 
inversion  by  a  twelfth,  into  the  Twelfth  and  Fifth,  respectively ;  the 
Eleventh  into  the  Second  ;  the  Tenth  into  the  Third  ;  etc. ;  and  vice 
versa. 


Inversion 
upwards. 


12. 


11. 


10. 


2.  1. 


xt                 — 

v 

z 

1 

VJT"  

1 

7-   ^1                    8.                        9.                      10.                          11.                    12. 

~&~              r\                                                                                        <~,                    S3 

jj 

K 

^  0> 

6.  -G>-   5. 


As  the  Sixth  becomes,  on  inversion,  a  Seventh,  it  must  always  be 
prepared  and  led  downward  by  a  step ;  as  a  passing-note  progressing 
downward,  it  needs  no  preparation.  E.  g., 


DOUBLE   COUNTERPOINT  IN  THE    TWELFTH. 


115 


Prepared  sixth. 


Unprepared  passiug  sixth. 


Double  counterpoint  in  the  twelfth  relies  principally  on  pro- 
gression by  thirds  or  tenths.  These  monotonous  combinations  must 
be  covered  up  as  skilfully  as  possible,  and  a  free  movement  must  be 
given  to  the  contrapuntal  part.  The  following  illustration  shows  the 
student  how  this  may  be  done.  To  begin  with,  we  write  thirds  and 
tenths  almost  exclusively  to  the  notes  of  the  cantus  firmus. 


259. 

c.  f. 


•g>~ 


F^=H2 «?- 


Now  the  counterpoint  is  developed  in  such  a  manner  as  to  cover 
up  the  progressions  in  thirds  and  tenths  as  much  as  possible ;  e.  g., 


26Oa. 
C.  f. 


/»r"1»7tJ"              fy 

*  g              —  ^~rfH~r  i~r 

\RY\\,    &>  *  

—  |  f      '      •            9      J      1   J      \               1      •   *         

—  \  j  v^U-  *    0    '        <  1—  ^^y  ' 

.__*•             &__« 

1  —  0  1  1  —  i  i  —  1 

H*)!    j\i  >9  

^Xbv/  — 



SE 


Of  this  example,  the  following  four  inversions  can  be  made. 


116  DOUBLE   COUNTERPOINT  IN  THE    TWELFTH. 

First  inversion.     The  counterpoint  is  inverted  to  the  twelfth  be- 
low ;  the  cantus  firmus  remains. 


C.  f. 

261. 

Cp. 


M 


^ 


-JttDtzj 


^: 
-s<- 


nn 


I=t=t 


F-*-f« 1 — 

1 — i — I -P— 

— H-4-- — 


-=n       \\=i 

— h" — & — tti <® 1 

I     i_ —Mtf. I 

I  f I I 


Second  inversion.     The  cantus  firmus  is  inverted  to  the  twelfth 
above  ;  the  counterpoint  remains. 


/ 

/L  I  *        ^ 

/ 

fmvp 

I 

262. 

/ 

V 

,  ^.,  —  ^--  —  i  ^j 

•«v 

^— 

—a  1  !  — 

—  p*  »- 

^_                       _| 

CD.      \ 

v  —  ^i|/fn~\  ^ 

J 

m   •  V   ' 

•P™"  «         ~^~         ~^r~ 

-P  -•-  •*•  4-    -F- 

1 1 1 1 — I— J— 


"•^ 1 


The  third  mode  of  inversion  is  merely  another  form  of  the  first. 


DOUBLE   COUNTERPOINT  IN  THE    TWELFTH. 


117 


The  cantus  firmus  is  set  an  octave  higher ;  the  counterpoint  a  fifth 
lower. 


C.  f. 

263  a.  ( 
Cp. 


f3    ' 


:     f:  -*-  *     - 
i=i:±=t^ 


etc. 


The  fourth  mode  of  inversion  is  another  form  of  the  second  ;   the 
cantus  firmus  is  set  a  fifth  higher,  the  counterpoint  an  octave  lower. 


C.  f. 


264. 


Cp. 


To  these  two-part  movements  a  third  free  part,  or  two  free  parts, 
can  be  added.  Example  260  b  is  an  illustration,  in  which  a  free  inner 
part  is  added  ;  also  the  inversion  263  6,  to  which  two  free  lower  parts 
are  added. 

The  cantus  firmus  is  set  an  octave  lower,  so  as  to  leave  room  for 
the  free  inner  part. 

. . J 

Cp. 


2606. 


C.  f. 


-r  --  m- 


ij **-! 1-,-J J .--J 


_i T. +—\-<2. 0 ?_ 


118 


DOUBLE   COUNTERPOINT  IN  THE   TWELFTH. 


2636.  ( 


rr-n 


xjJJUJ 

•         i m 


£) 

—  0.  —  =  

£) 

=S  P-*      »               . 

-a  •  

m            .  ... 

These  two  free  parts  may  also  be  utilized,  if  set  a  fifth  higher, 
for  the  inversions  of  Ex.  262. 

Triple  or  quadruple  counterpoint  in  the  twelfth  is  quite  as  impos- 
sible as  before,  in  counterpoint  in  the  tenth.  Should  one  desire  to 
add,  to  the  two  parts  in  double  counterpoint  in  the  twelfth,  a  third, 
or  third  and  fourth,  part,  the  latter  also  to  be  invertible  with  the 
first  two,  he  must  proceed  in  strict  accordance  with  the  rules  to  be 
observed  in  writing  quadruple  counterpoint  in  the  octave  ;  as  we  have 
done  in  Ex.  253.  All  the  suspensions  and  passing  dissonances  to  be 
avoided  in  the  last-named  species  of  counterpoint,  must  also  be 
avoided  here.  We  advise  the  student  to  begin  his  exercises  in  double 
counterpoint  in  the  twelfth  with  two  parts  only,  and  without  special 
consideration  of  the  exigencies  of  ordinary  two-part  writing.  To  each 
exercise  one  or  two  free  parts  may  be  added  ;  a  procedure  illustrated 
in  Exs.  260  b  and  263  6. 


PART   THE   THIRD. 


CHAPTER    XI. 

Counterpoint  in  Movements  containing  Five,  Six, 
Seven  or  Eight  Real   Parts. 

§  28.  Whereas,  in  three-  and  four-part  writing,  all  rules  and  pre- 
cepts governing  the  strict  style  must  be  rigidly  observed  in  order  to 
obtain  a  good  effect,  in  movements  containing  more  than  four  parts 
the  said  rules  are  greatly  relaxed.  The  greater  the  number  of  parts, 
the  freer  can  be  our  treatment  of  covered  fifths  and  octaves,  doubled 
leading-notes,  preparation  and  resolution  of  sevenths,  etc.  But,  in 
case  three-  or  two-part  episodes  are  introduced  in  the  midst  of  such  a 
movement,  the  rules  governing  three-  or  two-part  writing  remain  in 
force  throughout  the  episodes. 

In  seven-  and  eight-part  writing  the  two  lowest  parts  may  occa- 
sionally be  led  in  octaves  or  unisons  ;  e.  g., 


265. 


P3-2ZB                          2 

.                 -_ 

•       «               r 

SC 

I                i^ 

i        i        • 

1                            I 

'                ! 

1                              i 

i 
i 

!                • 

'        i                     i 

8%0  i-        ^ 

—  ^  1  

-*  *-         ^= 

., — «_ 


-na U 


120 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


Let  us  begin  by  examining  the  five-part  movement.  One  might, 
it  is  true,  give  the  additional  part  to  any  one  of  the  original  four ;  but 
it  is  best  to  write  either  two  sopranos  with  one  alto,  tenor  and  bass,  or 
one  soprano,  alto  and  tenor  with  two  basses.  Experience  shows  that 
in  most  choruses  the  soprano  voices  are  the  most  numerous,  and  that 
the  basses  are  usually  next  in  point  of  number.  Evidently,  then,  it 
is  better  from  the  standpoint  of  total  effect  to  divide  the  more  numer- 
ous sopranos  or  basses  into  two  sections  having  independent  parts, 
than  to  divide  the  strength  of  the  weaker  inner  parts,  which  are  in 
any  event  less  prominent.  For  the  same  reason,  the  cantus  firmus 
will  generally  be  set  in  the  bass  ;  less  often  in  the  soprano,  and  still 
seldomer  in  one  of  the  inner  parts.  In  unequal  counterpoint,  the  con- 
trapuntal movement  will  be  divided  up  among  the  several  parts, 
passing  from  one  to  another  in  alternation  ;  in  these  exercises  it  is  not 
best  to  let  one  part  alone  carry  out  this  movement.  A  five-part  com- 
position (Soprano  I  and  II,  Alto,  Tenor  and  Bass),  if  skilfully  written, 
will  be  highly  effective  on  account  of  its  full  harmonies. 


We  subjoin  an  illustration  of  the  five-part  style,  in  equal  counter- 
point ;  the  cantus  firmus  is  in  the  bass. 


266. 

Soprano  I. 


Soprano  II. 


Alto. 


Tenor 


Bass. 


XT    /  *       ^ 

^ 

1 

r^ 

1 

WEE. 

£r 

«?        1 

/i*    <j 

fp 

1 

Si*? 

1 

It* 

thf"  Tty  —  ^  — 

—  ^  

^?  

1 

1  f*  \i^ 

" 

1 

!     /4       ,              ^_ 

/^ 

^ 

/^J 

-_               I 

1     fj    /jl          ^r 

5_ 

D2 

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i 

' 

i 

pD«/u  — 

—  ^  

—  ^5  

—  El 

^r/\|-'    ^ 

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c.t 

^ 

FIFE-PA  RT  CO  UNTERPOINT. 


121 


The  same  cantus  firmus  might  be  worked  out,  in  unequal  counter- 
point, as  follows  : 


267. 

Soprano  I. 


Soprano  II. 


Alto. 


Tenor. 


Bass. 


tZI I 


(? 


-t— 


C.  f. 


The  same  cantus  firmus  with  more  rapid  figuration : 


268. 

Soprano  I. 


Soprano  II. 


Alto.      / 


Tenor. 


Bass. 


:| : 


S1$E 


C.  f. 


122 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


1%=-^— Sr 
n  <* 


m 


§29.  When  six  parts  are  employed,  the  best  disposition  of  the 
parts  will  be  to  divide  each  of  the  outer  parts  into  two  separate  divi- 
sions. We  shall,  therefore,  write  for  Soprano  I  and  II,  Alto,  Tenor, 
Bass  I  and  II.  The  cantus  firmus  of  Ex.  266,  worked  out  with  six 
parts,  might  be  presented  in  the  following  form  : 
269.  ^ . ,_  ^  -pg^j^- 


Soprano  I. 


Soprano  II. 


Alto. 


Tenor. 


Bass  I. 


Bass  II. 


SBate 


All. a- 

~cTf7 


"a.' 


m 


SIX-PART  COUNTERPOINT. 


123 


The  same  cantus  firmus,  with  more  rapid  counterpoint  in  the 
inner  parts : 
27Oa. 

Soprano  I. 


Soprano  II. 


Alto. 


Tenor. 


Bass  I. 


Bass  II. 


/r  vt*     <* 

^                            1 

\(^\\j 

T 

J 

tT 

n 

/>     ^ 

.— 

f-,    '                     »     ' 

II      SP 

"^ 

E 

03    ' 

-         J 

II3 

I 

^ 

«       •       P            1 

tfTTfJ1      » 

"& 

f 

no  IE 

!                 1 

'                                  "1 

113  -L             ^ 

•                                1 

^                •     T 

tBLzts 

'                  JB                 9 

f                         f     J 

11    t|; 

*        *                 0 

1       T 

'                                                     !              J 

«      p     -f- 

JS- 

-«>- 

y^"\  •                |fp 

~| 

nyy«/fi 

^^•^\1  ' 

'            1 

| 

[ff^I/U  — 

^^  

T-IST- 

KSln    <? 

3 

C.  f. 


-t: 


zit: 


1 


Of  course,  it  is  neither  necessary  nor  desirable  to  keep  all  six  parts 
moving  together  continuously ;  on  the  contrary,  the  effect  is  finer, 
when  individual  parts  pause  now  and  then  at  suitable  points,  or  when 
the  parte  enter  one  after  the  other,  as  in  the  following  illustration : 


124  COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 

2706. 


"Comfort  my  people/ 

Andante  sostenuto. 


Soprano  I. 


Soprano  II. 


Alto. 


Tenor. 


Bass  I. 


Bass  II. 


1  Jf  k 

fnV  (';      f*          & 

EE  —  3- 

!              'S*' 

1    »—  f      f= 

12 

TJ 

Saz        | 

\          !       i 

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**           1 

Tro  -   stet, 

tro  -  stet, 

tro  -  stet  mein 

Volk,.. 

dofce. 

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5 

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t^-U  

•     *" 

—  ,  — 

P            Tro     -      - 

.stet, 

tro    - 

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stet, 

— 

1  1                          ^2 

^j 

s^ 

•     v 

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*L./> 

tt 

"f     * 

olM  / 

\- 

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f      [     1 

dolce. 

TwtTTT  —  •  '  

^  _ 

—&  

~*  —  *  —  1 

"            V  J 

i      i     1 

Tro     -      - 

stet, 

tro    - 

stet, 

dolce. 

9       f 

ey 

-•-    *- 

y&~7~f  ••  — 

IB  

f                   | 

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-\  -1 

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, 

] 

Tro  -  stet  mein 

Volk,.. 

dolce. 

dolce. 

W-,   7T               ™ 

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• 

** 

1 

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1 

Tro 


XiJ  n          \               1 

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-£  1       ._ 

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—  ^  

-p  1 

{&"  ~  ^  — 

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^        tro  -  stet,      tro  -   stet      tro  -  stet  mein 

Volk 

U 

n/*o        A      A 

9 

k 

m 

Volk. 

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^^ 

i                 i 

1  

5 

iii 

1  • 

tro      -      -      stet, 

—  =: 

tro  -  stet  mein 

V 

= 

oik,  tro  -  stet  mein 

:_^   

r*  

0  — 

i  itl  V          ^^ 

11 

tro      -      -      stet,... 

-=i 

<p                   ~*~      •        - 

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1  1  1  — 

s^s 

1  1  

*y 

—  1 

•    stet. 

tro  -  stet  mein 

Volk 

SE VEN-PA RT  CO UNTERPOINT. 


125 


§30,  For  seven-part  writing  we  provide  two  sopranos  and  one  alto 

with  a  foundation  of  a  male  chorus  consisting  of  two  tenor  and  two 

bass  parts.     The  above  cantus  firmus  would  then  be  worked  out  thus  : 

271. 


Soprano  I. 

Soprano  II. 
Alto. 

Tenor  I.    \ 
Tenor  II. 

Bass  I. 

Bass  II. 

The* 
272. 

Soprano  I. 
Soprano  II. 

Alto. 
Tenor  I.    \ 

Tenor  II. 
Bass  I. 

BassII. 

7T19- 

{^ 

\           \           r 

HSSE 

L             1              r 

1 

i        £3 

GS 

& 

&            -^ 

^1 

h    '       h 

tl  'T^  — 



1             1 

S3                                                    S3                       S3                    ~&~ 

0      1 

11  ^  ^1^ 

1 

[I     £j     \\J 

1  1                    *t 

L                 L 

1 

^                                                        „                                                     -*-                             r              «                                   ,_«                                                -^ 

N                 {fe  



1 

II  4      .          x3 

-     ^ 

^_ 

s^i 

d  /  U       2 

•^ 

\ 

v 

~                 \ 

^             .            ^          -^         ~: 

1 

s^S 

| 

t^'0~ 

1 

i 

/^\  •  . 

.^J 

1 

l^y  'Vll 

—23  1 

^-^\  /      ^ 

k 

1  1  1  1  C*.  1  &  

C.  f. 

same  cantus  firmus  with  unequal  counterpoint  : 

ifiEzESa  —  ^-p2  —  (5'~ 

„    1  

-—  

W^  f 

^  —  :  

1 

^                X  N.                        '                                                        S  X 

—  TfT"^  — 

1  1          ^ 

\-^~  \ 

M      *.!  -/ 

)  j  /*    * 

1    • 

\                 \ 

NB. 

f^                    S3                     '      '                                  S3           S3                      S3        ~^~ 

&      \-     \                   T 

\^—\ 

II  /V  /)» 

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H;d  (  / 

1                                      H 

1                      K 

\                 \ 

j.               ^                /^                            ^,         /^                            /^       <^      7^' 

E^EI 

^  t 

!  ^  ZH 

1  1        ^ 

i     r  1  1     ' 

\i^" 
' 

L                                         1                                                LI 

1 

N.B. 

||4    ,       ,-", 

^2 

^)             1      ffl 

»J  /[»     °^ 

H     ib 

^J 

S2          1 

^I^u  —  ^  — 

—&  

& 

^•^  \b 

1 

' 

jf>)r^k  — 

-«"  h-z?  

1  1 

\^^\\L—^L  

:  \~-  

\-^ 

£32  —  1 

C.  f. 


126 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


A  suspension  resolving  upwards  by  a  whole-tone  step,  like  that  in 
the  alto  at  N.B.  in  the  last  measure  but  one,  is  permissible  in  strict 
writing  when  combined  with  a  suspension  resolving  downwards. 
(Compare  Manual  of  Harmony,  §55.)  And  the  covered  octave  over 
the  seventh,  occuring  at  N.B.,  same  measure,  beween  Tenor  I  and 
Soprano  I,  is,  like  all  other  covered  fifths  and  octaves,  permitted  when 
as  many  as  seven  parts  are  present.  The  upward  progression  of  a 
diminished  fifth  to  a  perfect  fifth, 


forbidden  in  four-part  writing,  is  also  allowed  here,  as  well  as  octaves 
and  unisons  in  contrary  motion  : 


/L 

i        1 

sy<z 

rt\ 

1         X= 

The  above-mentioned  covered  octave  over  the  seventh  might,  however, 
easily  be  avoided  by  writing  D  instead  of  G  as  the  last  note  but  one 
in  the  first  tenor. 

Below  we  give  the  same  cantus  finnus  with  a  more  rapid  counter- 
point : 


a                 T 

>     /*      & 

,       r    - 

• 

fr'vvx 

r 

\i7 

L                          !.     ^ 

1 

0 

^" 

"^ 

i       ^ 

<&• 

G/ 

ZH 

Soprano  II. 

ii     *•  V 

1  13 

,^j 

s? 

JO- 

fe£& 

. 

Alto. 

fl-W-iK  





<y 

j 

IL4-,,       ^ 

j-'    - 

1"  /  * 

E. 

l|; 

Wi        — 

—  , 

Tenor  II. 

/  *             •                 • 

^ 

,                    /' 

I)-/ 

**** 

(y 

/•V  i      *              & 

f^i 

Bass  I. 

iCJ'/  * 
C-?t|7     T 

V\'  1 

f2 

Bass  II. 

^^(fy"  —  ^  

C.f. 


SEVEN-PART  COUNTERPOINT. 


127 


^k"  



VM/ 

1 

t> 

— 

~~~^ 

f^ 

« 

^                   <^- 

^>       i 

-    ' 

r 

, 

;  ' 

1 

D3 

I 

Jja 

•      r51 

& 

~V             ^ 

-  o        i 

II                II 

;  j 



ii        ^ 

s~ 
m          m 

~^        •  p  •*" 

1 

Wa- 

-0    p  — 

-+-               ff-T  •__! 

1 

tt"  

—  —  1  1  

1 

• 

1 

th*  Z2  1 

tt3          

—  &  

o*  •                       |-    - 

1 

1 

fo}'             '                    m 

0 
^ 

«>* 

—7S—       \ 

<£J'                                 • 

1 

^      .  1  

- 

1 

(^  — 

1 

-a  — 

When  composing  a  piece  for  seven  parts,  it  is,  on  the  whole,  best 
to  regard  it  as  consisting  of  a  double  chorus — a  female  chorus  with 
two  sopranos  and  one  alto,  and  a  four-part  male  chorus  with  two  tenors 
and  two  basses.  These  two  choruses  may  then  be  employed  either  in 
alternation  or  simultaneously,  as  the  following  illustration  shows : 

"How  fair  are  Thy  tabernacles,  Lord  Sabaoth." 


274. 

Soprano  I.    J 

Soprano  n.  \ 
Alto. 

Tenor  I. 

Tenor  n. 
/ 

\ 

Bass  I. 
Bass  II. 

•  *  h— 

r   —  1  —  —  1~ 

—  ~^y  — 

ft)    -*4.     * 

-P  

H  3  .      &  - 

—  c  *  — 

Wie  schon  sind  dei  -  ne     Zel    -    te,        Herr, 

L_        dolce    .-                  -                                    .         .      . 
rt  Kf*                                                                                ' 

Ze    -  ba  - 

)                   I 

-&     * 

•  «  •  — 

r~5       T"     ! 

1 

•^ 

11                   dnlgf 

| 

ri     f*       A       1  ^3 

1 

'       ^ 

ffB-tr^  —  t  —  F  —  '  —  ' 

*  »  m— 

-&-?—&—- 

—&>—- 

—  H—  \—f  

k 

i                                      1                  '     ^ 

dolce. 

U  -^  ly       C* 

—                   1            ^ 

1    ^  V  -rt  *  ^        "** 

™    •                1            "•  • 

m   > 

I         **^ 

1 

\                              ~ 

9E 

L 

k 

Wie 

tt5«t2 

•                   1           i"           1 

p-™  —  ^ 

:  —  •  *  — 

4- 

1                         1 

y^A  .    L.    rt 

|cy«.    [/    tl        N» 

^    -                 j_           ^  - 

™   "**   ~       ^ 

^—9~\jt^  

f-  

1  — 

y^A«    L    f* 

[cy-i  17  t»     v» 

^B      • 

^^  • 

—  •  —  s 

_ 

^ta^h  „/!       ^ 

J 

128  COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


-rb: 


— ^-«~- *- 


•      v,    -       •     [    I          I      |  ~f 


oth! 


Wie     schon      sind  dei-ne 


t=J=j 


_  - 


3=»=5=? 

-*s> 1 — i — ^ — (- 


=Bt 


i  ^,  ~ 


wie  schon 


^gg^gy^B^ 


schon    sind  dei-ne      Zel  -  te,      ,  Herr,       Ze  -  ba  -  oth,  wie  schon  sind 


-<^--—0—0—»— 


=t= 


-<2_?- 


m 


'il^H^—     -s—  s-^ 

=&  •     r- 

ffi^ 

*/             Zel        -        -        -      te,  

Herr,        Ze    -    ba 

-  oth! 

gy    • 

jj      K                  ^        •                                                                                 t*        ' 

1 

—  -P      l>             —  *                                                                                          ^> 

1 

-H  1 

1 

-S>-  . 

L                                                      ^                ^ 

--P  1  .  

1  1 

1  ll'J^—t  —•  —                                                   —  1  

1 

^  1  1          [/ 

1                         1 

sind       dei    -    ne        Zel    -    -    te,     Herr,        Ze    -    ba 

L                                             _                                                                      /y             & 

-    oth! 

.[].*,'             -~                             ~               j^                  £ 

I       *^      •                 I 

\\  **  /     ri 

^>      • 

1                  1 

]J                '                                                      , 

1                  1 

dei        -        -    ne        Zel            te,    Herr,        Ze    -    ba 

-  oth! 

1111?  U                                              *       9             i 

i 

^             1 

'                                            •                             i       1    i                             ' 

wie        schon,  Heir,        Ze    -    ba 

-  oth! 

Sit  —  *  ~~"  —  *~         *  • 

—&  '  ^  * 
—  i  1  — 

schon,...          wie         schon,  Herr,      Ze    -      ba 

-  oth! 

fm\'  k                                       "     r 

i                  1 

S2S  /         •                                                                            i 

S^BUC:                          xJ                                -J—\ 

wie      schon, 


Herr,        Ze    -  ba  -    oth! 


EIGHT-PART  COUNTERPOINT. 


129 


§31.  In  eight-part  writing  there  are  two  parts  for  each  kind  of  voice. 
But  one  chorus  of  eight  parts  is  not  so  often  employed  as  two  'four- 
part  choruses,  singing  together  or  alternately.  We  may  now  permit 
the  basses  (lowest  parts)  of  either  chorus  to  move  occasionally  in 
unisons  or  octaves ;  the  sopranos  (highest  parts)  of  either  are  also 
sometimes  led  in  unisons ;  or  the  two  choruses  are  treated  so  as  to 
form  only  one  four-part  chorus.  All  these  liberties  are  necessary  on 
account  of  the  extreme  difficulty  encountered  in  leading  eight  real 
parts  quite  independently  for  any  length  of  time.  As  a  model  to  be 
followed  by  the  student  in  eight-part  exercises,  we  first  give  a  work- 
ing-out of  the  cantus  firmus  already  employed  in  all  the  four-part 
examples ;  our  first  illustration  being  in  equal  counterpoint.  The 
student  must  take  care  not  to  lead  any  two  parts  in  parallel  octaves  or 
perfect  fifths. 


275. 

Soprano  I. 


Soprano  II. 


Alto  I. 


Alto  II. 


Tenor  I. 


Tenor  II. 


Bass  I. 


Bass  n. 


yr  i  » 

taSJU 

\u)^ 

cT 

S^J 

^~ 

ZB 

s^ 

1C 

" 

J3-. 

^. 

Jd. 

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1 

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£) 

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1 

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1 

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r*   i 

^j 

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^s 

1 

ttfl  /» 

-^ 

"^ 

1 

V|y 

1 

tt-x  ^  1 

ptztt      £ 

^  

—  ^ 

•$>  

—  ($J  

—fr  

1 

Vb 

<^" 

1 

-1S>- 

-^5>- 

/^\«    , 

EEZsZI! 

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^^•^  »|y 

-^ 

' 

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-~ 

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—^ 

IV 

130 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


The  same  cantus  firmus  with  unequal  counterpoint. 
276.  , — , 


Soprano  I. 


Soprano  II. 


Alto  I. 


Alto  II. 


Tenor  I. 


Tenor  II. 


Bass  I. 


Bass  II. 


S^ 


fc±=t±ZI±Z 


1^ 


-=££=&- 

=it=t 


^=1 


^ffF 


at 


'-ig- 


Z2I 


C.f. 


Should  one  desire  to  employ  figurate  counterpoint  in  eight-part 
writing,  he  must  carefully  avoid  bringing  the  passing  dissonant  tones 
into  too  close  proximity  with  the  chord-tones,  in  order  that  the  har- 
mony may  always  appear  clear.  An  illustration  follows,  with  the 
familiar  cantus  firmus. 


EIGHT-PART  COUNTERPOINT. 


131 


277. 

-&•                 *          &-            -\   &            —  & 

S3 

Soprano  I. 



w 

^            <^ 

1                                                .    .  ,     & 

r>      • 

Soprano  II. 

TV 

11       *K 

: 

||4 

r 

-S-                                                         -22. 

I 

Alto  I. 

i  >  Zp 

I 

ttaSpzzz 



_,                               " 

AltoII. 

pa  |p 

.,                     ~~"                                                            ~~     ^  m                                  O 

3    i                                                           ]    f-           m 

^    .                 r 

Tenor  I. 

fta  ZQ 

i                        | 

11    ip 

1                                                                        1                     ! 

1 

-»     ,          --,                                                           1 

^ 

m            TT 

D'ovtv     f>   •                          '•!,;.                   i 

1      1                                 '1 

-f-          «         , 

-G>- 

Bass  I. 

[^/•/ti         1                        [                                                               ^"^ 

*^^  v|y                             ' 

'                                                                                     ' 

Bass  II 

f^\*     '                                                                                                              f^ 

L^y  */  1  *                                                                                                                      ^^ 

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52  — 

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i 

l&  —  -5 

^— 

132 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


In  free  composition,  all  the  liberties  enumerated  above  are 
brought  into  play ;  so  that  the  sopranos  or  altos,  tenors  or  basses, 
may  be  written  in  unison,  or  the  entire  chorus  set  for  only  four  parts. 
An  example  of  this  style  of  work  follows : 


273. 


Soprano  I  &  II. 


Alto  I  &  II. 


Tenor  I  &  II. 


Bass  I  &  II. 


molt'  espr. 


EIGHT-PART  COUNTERPOINT. 
~  dolcisg. 


133 


men,     a 


men,     a 


m 


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&  0 i-S^ 


men, 


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1P  dolciss. 


men,  a 


men,          a 


dolcisg. 


men, 


j  "VJ  O/COU.  J  .  \ 


a  -  men,      a  -  men, 
-^ j-r-B^^I-i^ 


:^= 


-r-^T" — r 


— <5> -^.~ 


-^ 1-,5,-i- 


134 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


A  grander  effect  can,  however,  be  obtained  by  writing  for  two 
four-part  choruses ;  an  illustration  of  such  a  double  chorus  is  sub- 
joined : 


279. 

Soprano. 

Alto. 
Tenor. 

Bass. 

Soprano. 
Alto. 
Tenor. 
Bass. 

Allegro  moderate. 

r\*       J                                    !     i               fc.                * 

Second  Chorus.  First  Chorus. 

zfV-^" 

{•^ 

1       •* 

33D  ~_—  J             J 

&.       • 

f/Tv    1  j       Z 

•         9   »    *   1      0        • 

VM./ 

i 

tr 

Jauch  - 
Praise 

zet, 

ye, 

jauch     -      -      zet   dem 
praise  ye     the 

Herrn, 
Lord, 

i     if"        ^^^ 

1  /%    i  *     I 

t                 N* 

U  a     \  j      \ 

1                               ! 

1 

Jauch  - 
Praise 

zet,           jauch    -     zet      dem           Herrn, 
ye,           praise         ye       the            Lord, 

[j~3^7"T  —  ^  — 

•              N* 

-*-*—*-0    '  m     0  g— 

l~  •  

f*i  / 

1*            ' 

Jauch  - 
Praise 

zet, 

ye, 

jauch     -      -      zet   dem 
praise  ye     the 

Herrn, 
Lord, 

f^\  !**                 ^2                    ' 

£^      •                                         ^ 

(?                       1 

(^^•if^J 

i                        -* 

r             _ 

^^^    \  y 

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1                          1 

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1 

Jauch  - 
Praise 

fi  tr 

zet,         jauchzt                 dem 
ye,          praise                   the 

Herrn, 
Lord, 

V  '* 

I 

XT       /  »            ]                             x* 

fZ*                     1        "•• 

i£ft—  ^  —  S^  0  — 

•  — 

Jauch  - 
Praise 

zet, 

ye, 

jauch  -  zet, 
praise      ye, 

aj 

/*"                       1 

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—  *  •£  — 

^        7K" 

1 

1 

Jauch  - 
Praise 

zet, 

ye, 

jauch  -  zet, 
praise      ye, 

—  *  —  —  1 

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t       \t 

—  d 

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iff                                 I 

1 

Jauch  - 
Praise 

zet, 

ye, 

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praise      ye, 

y^\«ff 

1 

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[C^*T1/   * 

i           •*• 

^* 

^^    *  ;            ! 

—  i  —  —  | 

Jauch  - 
Praise 

zet, 

ye, 

jauch  -   zet, 
praise      ye, 

DOUBLE   CHORUS. 


135 


ff. 


1  .jfJi.  —  —  

-0  —  p  —  •  —  ^  —  •  0— 



irK 

\~\) 

9 

al       -                         le 
praise   His 

Welt, 
name, 

cresc 

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ii     5                      mm 

r      riii 

B3 

mmmmf^s^^  

!_ 

al      -        -        -      le 
praise  His 

Welt, 
name, 

,^-f 

cresc. 

] 

1  1  V            *>*                               j 

J 

0 

1 

jauch    -    zet, 
praise         ye 

-&-  •                   -0- 

al     -        -        -      le 
all  His 

Welt, 
name, 

ff 

cregc. 

^s^*     1 

^      •                                               £ 

\ 

££*  —  '-  

-*  -1 

\                                                                                                                                                 i 

jauch     -        -     zet,            al              -        -      le         Welt, 
praise                   ye             all                            His        name, 

fg                                                                                                       C«IC.                                           ff       _ 

j                                  | 

'     1        ^     A     '                    A 

*-£-  •m—0-m-  0  f-  — 

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jauch    -     -     zet  dem  I 
praise                ye    the  1 

-t/  

[errn,      al        -        le, 
jord,    praise             ye 

al    -        -        -    le 
all  His 

ff 

-^ 

i          1 

Sz: 

— 

:  J 

-1—  '  H 

jauch    -     zet     dem         Herrn,                                      al      -               le 
praise         ye      the           Lord,                                    praise                 His 

M             9>  0        •                     0                     CregC'                              ff 

• 

II                      1            ll|                      U 

1  ^                 ^ 

Q. 

—  3  —  ^^••J  —  ^|  —  i^  — 

jauch     -      -      zet   dem  I 
praise  ye    the  ] 

[errn,      al        -         le          Welt, 
jord,     praise            His         name, 

cresc.                               -ff 
m           &  '     -i 

£-7                                       I* 

-1  ^ 

?2— 

jauch    -    zet            dem  Herrn,      al        -         le 
praise         ye              the  Lord,    praise             ye 

Welt,         dem 
all             His 

136 


COUNTERPOINT  IN  MORE    THAN  FOUR  PARTS. 


/3r-r-^ 

~a  —  ;  —  0  —  »  — 

^"       >*  1 

SF^ 
tr     B^« 

jauch 
praise 

—  *  —  ! 

•BUM           «**           ' 

zet  dem 
ye    the 

-\  P*  j      ,  •  *-  -)i-i_*-| 

'  >^_>    •  a            ' 

Herren,  dem  Herrn,      dem        Herrn. 
Lord,       the  Lord,        the        Lord. 

l*  '               P 

H-    -#        /S> 

-*  *  —  •      ,.              —  p— 

P.—1  

-^    *-jc-| 

I     ^ 

1 

jauch 
praise 

»& 

-    zet               dem    Herren, 
ye                  the     Lord, 

(P                                         f-* 

«    • 

-»—  T- 

1  

i 

-s-l 

—  8—  '  

1              1 

jauchzt 
praise 

dem            Herrn,              dem                       Herrn. 
ye                all                   His                .        name. 

(<t)i8  —  ^^  -=VT—  i  — 

*^»-^                                                               i                    i 

i              1 

9 

'              | 

al 
praise 

n  *»       "^" 

le 
ye 

Welt                              dem          Herrn. 
all                                His           name. 

—  I  —  i  —  i  v»  

—  *  —   —  *  —  ?  *  —  ~m  ?  — 

:  —  >»H 

9g9                £ 

-4-           '  —  (-        |  •  —  *        )-. 

~^~  ^  1 

Welt. 

—  teH^HM^  ^  U1  V  

jauch                    -    zet      dem 

nraisf>    .                      ..   VA        t.h« 

Herrn. 
Lord. 

name, 

—  #  —  ^  

f—  pH=    '     -                                  ^^  

^        y     1 

_^  — 

^—^1 

\> 

^^^r 

•T  1 

Welt,    jauch        -        zet    dem  Herrn,                             dem        Herrn. 
name,  praise                 ye      the    Lord,                             the          Lord. 

0=  *   - 



(^  *   ^*  1 

9 

jauch 
praise 

1 

zet                            dem            Herrn. 
ye                            His            name. 

^A^*^t 

f^y  «^J 

*VT-' 

Herrn, 
name, 

dem                                              Herrn. 
His                                               name. 

When  writing  thus  in  eight  parts  for  two  choruses,  it  is  well  to 
treat  the  parts  belonging  to  the  first  chorus  as  Soprano  I,  Alto  I,  etc., 
and  those  belonging  to  the  second  chorus  as  Soprano  II,  Alto  II,  etc., 
the  latter  being  set  correspondingly  lower. 


CLOSING  SUGGESTIONS. 


137 


In  his  exercises  in  five-,  six-,  seven-,  and  eight-part  writing,  the 
student  may  take  for  a  foundation-part  (best  set  in  the  bass)  any 
suitable  cantus  firmus  used  in  former  exercises.  Later  he  should 
attempt  to  invent  original  movements  of  this  description,  in  the  form 
of  short  motets  in  the  strict  style.  And  now  that  he  has  become 
familiar  with  the  rules  of  counterpoint,  it  is,  of  course,  extremely  im- 
portant, and  will  be  of  the  highest  utility,  for  him  to  study  attentively 
the  works  of  the  classic  masters :  Bach,  Handel,  and  others.  For 
only  by  means  of  such  study  can  he  reap  the  full  benefit  of  the  fore- 
going contrapuntal  course. 

We  add  a  few  additional  basses  peculiarly  adapted  for  founda- 
tion-parts in  movements  exceeding  four  parts.  The  student  should 
work  them  out,  to  begin  with,  in  equal  counterpoint,  and  later  in  un- 
equal counterpoint,  with  five,  six,  and  more  parts. 


rzf^g 


[Special  attention  is  called  to  the  fact,  that  the  "Explan- 
atory Remarks  and  Suggestions"  added,  by  Doctor  Jadas- 
sohn  to  the  Third  German  Edition,  in  the  shape  of  an 
Appendix,  have  been  interpolated,  in  the  present  transla- 
tion, in  their  proper  places  in  the  body  of  the  book.  As  this 
arrangement  greatly  facilitates  the  use  of  the  work,  it  can 
hardly  fail  to  meet  with  the  approval  of  both  teachers  and 
Students. — TBANSLATOE'S  NOTE.] 


119025 


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